Finiteness Criteria in Quasi-resolving Subcategories View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-03-08

AUTHORS

Houjun Zhang, Xiaoguang Yan

ABSTRACT

Quasi-resolving subcategory, as a generalization of resolving subcategory, was introduced in Zhu (J Algebra 414:6–40, 2014). Let A be an abelian category, X a quasi-resolving subcategory of A and H an Ext-injective cogenerator for X. We study the subcategory consisting of all the objects with finite X-resolution dimension. Furthermore, we investigate the objects with approximations by objects which are either with finite H-resolution dimension or else in X. As applications, we give the finiteness criteria of the homological dimensions in Gorenstein categories of modules and complexes. More... »

PAGES

1-16

References to SciGraph publications

  • 2000. Gorenstein Dimensions in NONE
  • 2013-08. Resolving Resolution Dimensions in ALGEBRAS AND REPRESENTATION THEORY
  • 1995-12. Gorenstein injective and projective modules in MATHEMATISCHE ZEITSCHRIFT
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s41980-019-00215-5

    DOI

    http://dx.doi.org/10.1007/s41980-019-00215-5

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1112634662


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Pure Mathematics", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Mathematical Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Nanjing University", 
              "id": "https://www.grid.ac/institutes/grid.41156.37", 
              "name": [
                "Department of Mathematics, Nanjing University, 210093, Nanjing, China"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Zhang", 
            "givenName": "Houjun", 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Nanjing Xiaozhuang University", 
              "id": "https://www.grid.ac/institutes/grid.440845.9", 
              "name": [
                "School of Information Engineering, Nanjing Xiaozhuang University, 211171, Nanjing, China"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Yan", 
            "givenName": "Xiaoguang", 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "https://doi.org/10.1080/00927872.2011.622326", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1002306714"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.jalgebra.2005.12.007", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003564530"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1112/s0024611502013527", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1009223934"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1080/00927872.2015.1044100", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1009918015"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1112/jlms/jdm124", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1014235527"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1017/s1446788708000761", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019090253"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1080/00927871003741497", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1021651245"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bfb0103980", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1022227228", 
              "https://doi.org/10.1007/bfb0103980"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bfb0103980", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1022227228", 
              "https://doi.org/10.1007/bfb0103980"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02572634", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024840797", 
              "https://doi.org/10.1007/bf02572634"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02572634", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024840797", 
              "https://doi.org/10.1007/bf02572634"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.jalgebra.2014.05.018", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1027859321"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1080/00927879808826229", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1028832841"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10468-012-9351-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1039097353", 
              "https://doi.org/10.1007/s10468-012-9351-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.jpaa.2003.11.007", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043741469"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1080/00927872.2016.1235173", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1058289334"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/s0002-9947-2014-06007-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1059336120"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/memo/0094", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1059343143"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1142/s1005386713000576", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1063013230"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2019-03-08", 
        "datePublishedReg": "2019-03-08", 
        "description": "Quasi-resolving subcategory, as a generalization of resolving subcategory, was introduced in Zhu (J Algebra 414:6\u201340, 2014). Let A be an abelian category, X a quasi-resolving subcategory of A and H an Ext-injective cogenerator for X. We study the subcategory consisting of all the objects with finite X-resolution dimension. Furthermore, we investigate the objects with approximations by objects which are either with finite H-resolution dimension or else in X. As applications, we give the finiteness criteria of the homological dimensions in Gorenstein categories of modules and complexes.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/s41980-019-00215-5", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1223581", 
            "issn": [
              "1017-060X", 
              "1018-6301"
            ], 
            "name": "Bulletin of the Iranian Mathematical Society", 
            "type": "Periodical"
          }
        ], 
        "name": "Finiteness Criteria in Quasi-resolving Subcategories", 
        "pagination": "1-16", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "55b4a1b67a3cad4dc4b7812dec08efec949b612e9f67fc69026021f0d23da572"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s41980-019-00215-5"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1112634662"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s41980-019-00215-5", 
          "https://app.dimensions.ai/details/publication/pub.1112634662"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T11:20", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000354_0000000354/records_11719_00000002.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://link.springer.com/10.1007%2Fs41980-019-00215-5"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s41980-019-00215-5'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s41980-019-00215-5'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s41980-019-00215-5'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s41980-019-00215-5'


     

    This table displays all metadata directly associated to this object as RDF triples.

    117 TRIPLES      21 PREDICATES      41 URIs      16 LITERALS      5 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s41980-019-00215-5 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author N55e33db87b3342d7bc75e766458ff875
    4 schema:citation sg:pub.10.1007/bf02572634
    5 sg:pub.10.1007/bfb0103980
    6 sg:pub.10.1007/s10468-012-9351-5
    7 https://doi.org/10.1016/j.jalgebra.2005.12.007
    8 https://doi.org/10.1016/j.jalgebra.2014.05.018
    9 https://doi.org/10.1016/j.jpaa.2003.11.007
    10 https://doi.org/10.1017/s1446788708000761
    11 https://doi.org/10.1080/00927871003741497
    12 https://doi.org/10.1080/00927872.2011.622326
    13 https://doi.org/10.1080/00927872.2015.1044100
    14 https://doi.org/10.1080/00927872.2016.1235173
    15 https://doi.org/10.1080/00927879808826229
    16 https://doi.org/10.1090/memo/0094
    17 https://doi.org/10.1090/s0002-9947-2014-06007-8
    18 https://doi.org/10.1112/jlms/jdm124
    19 https://doi.org/10.1112/s0024611502013527
    20 https://doi.org/10.1142/s1005386713000576
    21 schema:datePublished 2019-03-08
    22 schema:datePublishedReg 2019-03-08
    23 schema:description Quasi-resolving subcategory, as a generalization of resolving subcategory, was introduced in Zhu (J Algebra 414:6–40, 2014). Let A be an abelian category, X a quasi-resolving subcategory of A and H an Ext-injective cogenerator for X. We study the subcategory consisting of all the objects with finite X-resolution dimension. Furthermore, we investigate the objects with approximations by objects which are either with finite H-resolution dimension or else in X. As applications, we give the finiteness criteria of the homological dimensions in Gorenstein categories of modules and complexes.
    24 schema:genre research_article
    25 schema:inLanguage en
    26 schema:isAccessibleForFree false
    27 schema:isPartOf sg:journal.1223581
    28 schema:name Finiteness Criteria in Quasi-resolving Subcategories
    29 schema:pagination 1-16
    30 schema:productId N1c95c93cb0944c619e4f875074df1d59
    31 N5b1410e2f96e411d883a64722b42158a
    32 Nc4e8c87972aa4ab4baf79aef46b06dba
    33 schema:sameAs https://app.dimensions.ai/details/publication/pub.1112634662
    34 https://doi.org/10.1007/s41980-019-00215-5
    35 schema:sdDatePublished 2019-04-11T11:20
    36 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    37 schema:sdPublisher N9464a46783aa48be88ea567a789d6fc3
    38 schema:url https://link.springer.com/10.1007%2Fs41980-019-00215-5
    39 sgo:license sg:explorer/license/
    40 sgo:sdDataset articles
    41 rdf:type schema:ScholarlyArticle
    42 N1c95c93cb0944c619e4f875074df1d59 schema:name doi
    43 schema:value 10.1007/s41980-019-00215-5
    44 rdf:type schema:PropertyValue
    45 N4cbad5fc0a294cb9bcc0cde70461c2c9 schema:affiliation https://www.grid.ac/institutes/grid.440845.9
    46 schema:familyName Yan
    47 schema:givenName Xiaoguang
    48 rdf:type schema:Person
    49 N55e33db87b3342d7bc75e766458ff875 rdf:first N9478dfdb75a842678f6d7f40075fb3a3
    50 rdf:rest Ncfe3cc268e6f4c688e095b7962b605d8
    51 N5b1410e2f96e411d883a64722b42158a schema:name readcube_id
    52 schema:value 55b4a1b67a3cad4dc4b7812dec08efec949b612e9f67fc69026021f0d23da572
    53 rdf:type schema:PropertyValue
    54 N9464a46783aa48be88ea567a789d6fc3 schema:name Springer Nature - SN SciGraph project
    55 rdf:type schema:Organization
    56 N9478dfdb75a842678f6d7f40075fb3a3 schema:affiliation https://www.grid.ac/institutes/grid.41156.37
    57 schema:familyName Zhang
    58 schema:givenName Houjun
    59 rdf:type schema:Person
    60 Nc4e8c87972aa4ab4baf79aef46b06dba schema:name dimensions_id
    61 schema:value pub.1112634662
    62 rdf:type schema:PropertyValue
    63 Ncfe3cc268e6f4c688e095b7962b605d8 rdf:first N4cbad5fc0a294cb9bcc0cde70461c2c9
    64 rdf:rest rdf:nil
    65 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    66 schema:name Mathematical Sciences
    67 rdf:type schema:DefinedTerm
    68 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    69 schema:name Pure Mathematics
    70 rdf:type schema:DefinedTerm
    71 sg:journal.1223581 schema:issn 1017-060X
    72 1018-6301
    73 schema:name Bulletin of the Iranian Mathematical Society
    74 rdf:type schema:Periodical
    75 sg:pub.10.1007/bf02572634 schema:sameAs https://app.dimensions.ai/details/publication/pub.1024840797
    76 https://doi.org/10.1007/bf02572634
    77 rdf:type schema:CreativeWork
    78 sg:pub.10.1007/bfb0103980 schema:sameAs https://app.dimensions.ai/details/publication/pub.1022227228
    79 https://doi.org/10.1007/bfb0103980
    80 rdf:type schema:CreativeWork
    81 sg:pub.10.1007/s10468-012-9351-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039097353
    82 https://doi.org/10.1007/s10468-012-9351-5
    83 rdf:type schema:CreativeWork
    84 https://doi.org/10.1016/j.jalgebra.2005.12.007 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003564530
    85 rdf:type schema:CreativeWork
    86 https://doi.org/10.1016/j.jalgebra.2014.05.018 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027859321
    87 rdf:type schema:CreativeWork
    88 https://doi.org/10.1016/j.jpaa.2003.11.007 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043741469
    89 rdf:type schema:CreativeWork
    90 https://doi.org/10.1017/s1446788708000761 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019090253
    91 rdf:type schema:CreativeWork
    92 https://doi.org/10.1080/00927871003741497 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021651245
    93 rdf:type schema:CreativeWork
    94 https://doi.org/10.1080/00927872.2011.622326 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002306714
    95 rdf:type schema:CreativeWork
    96 https://doi.org/10.1080/00927872.2015.1044100 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009918015
    97 rdf:type schema:CreativeWork
    98 https://doi.org/10.1080/00927872.2016.1235173 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058289334
    99 rdf:type schema:CreativeWork
    100 https://doi.org/10.1080/00927879808826229 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028832841
    101 rdf:type schema:CreativeWork
    102 https://doi.org/10.1090/memo/0094 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059343143
    103 rdf:type schema:CreativeWork
    104 https://doi.org/10.1090/s0002-9947-2014-06007-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059336120
    105 rdf:type schema:CreativeWork
    106 https://doi.org/10.1112/jlms/jdm124 schema:sameAs https://app.dimensions.ai/details/publication/pub.1014235527
    107 rdf:type schema:CreativeWork
    108 https://doi.org/10.1112/s0024611502013527 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009223934
    109 rdf:type schema:CreativeWork
    110 https://doi.org/10.1142/s1005386713000576 schema:sameAs https://app.dimensions.ai/details/publication/pub.1063013230
    111 rdf:type schema:CreativeWork
    112 https://www.grid.ac/institutes/grid.41156.37 schema:alternateName Nanjing University
    113 schema:name Department of Mathematics, Nanjing University, 210093, Nanjing, China
    114 rdf:type schema:Organization
    115 https://www.grid.ac/institutes/grid.440845.9 schema:alternateName Nanjing Xiaozhuang University
    116 schema:name School of Information Engineering, Nanjing Xiaozhuang University, 211171, Nanjing, China
    117 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...