Notes on Gorenstein Flat Modules View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2018-10-15

AUTHORS

Yanjiong Yang, Xiaoguang Yan

ABSTRACT

In this paper, we explore conditions under which Gorenstein flat modules are Gorenstein projective. We prove that all countably presented strongly Gorenstein flat modules are Gorenstein projective over perfect rings. Moreover, we show that if the base ring R is ∑-pure injective as an R-module, then the class of Gorenstein flat modules coincides with the class of Gorenstein projective modules, and hence all modules have Gorenstein projective covers. And as a corollary, we give a characterization of coherent perfect rings by Gorenstein projective and Gorenstein flat modules. More... »

PAGES

1-8

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s41980-018-0135-5

DOI

http://dx.doi.org/10.1007/s41980-018-0135-5

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1107645880


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": "Taizhou University", 
          "id": "https://www.grid.ac/institutes/grid.440657.4", 
          "name": [
            "Department of Mathematics, Taizhou University, 225300, Taizhou, China"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Yang", 
        "givenName": "Yanjiong", 
        "id": "sg:person.013032465253.38", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013032465253.38"
        ], 
        "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", 
        "id": "sg:person.010315142607.97", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010315142607.97"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1080/00927872.2015.1027380", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1012527708"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.jalgebra.2012.09.018", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1017221364"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s10468-016-9626-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1021471910", 
          "https://doi.org/10.1007/s10468-016-9626-3"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s10468-016-9626-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1021471910", 
          "https://doi.org/10.1007/s10468-016-9626-3"
        ], 
        "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.jpaa.2006.10.010", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1032037039"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1112/jlms/jdr014", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1032222200"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1006/jabr.1996.6882", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1033692641"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1080/00927872.2013.780064", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1038640617"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1515/9783110199727", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1050747020"
        ], 
        "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/10.1512/iumj.2008.57.3325", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1067513769"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.5486/pmd.2017.7689", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1091320859"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1515/9783110803662", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1096920672"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2018-10-15", 
    "datePublishedReg": "2018-10-15", 
    "description": "In this paper, we explore conditions under which Gorenstein flat modules are Gorenstein projective. We prove that all countably presented strongly Gorenstein flat modules are Gorenstein projective over perfect rings. Moreover, we show that if the base ring R is \u2211-pure injective as an R-module, then the class of Gorenstein flat modules coincides with the class of Gorenstein projective modules, and hence all modules have Gorenstein projective covers. And as a corollary, we give a characterization of coherent perfect rings by Gorenstein projective and Gorenstein flat modules.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s41980-018-0135-5", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1223581", 
        "issn": [
          "1017-060X", 
          "1018-6301"
        ], 
        "name": "Bulletin of the Iranian Mathematical Society", 
        "type": "Periodical"
      }
    ], 
    "name": "Notes on Gorenstein Flat Modules", 
    "pagination": "1-8", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "d0753a44a1d742ab75011b636140bea7b85fa2e0aea2416d791169507039a74c"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s41980-018-0135-5"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1107645880"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s41980-018-0135-5", 
      "https://app.dimensions.ai/details/publication/pub.1107645880"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T02:23", 
    "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/v90/0000000001_0000000264/records_8700_00000562.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://link.springer.com/10.1007%2Fs41980-018-0135-5"
  }
]
 

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/s41980-018-0135-5'

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/s41980-018-0135-5'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s41980-018-0135-5'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s41980-018-0135-5'


 

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

106 TRIPLES      21 PREDICATES      37 URIs      16 LITERALS      5 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s41980-018-0135-5 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N9eb780cb225240e1a033aedad7ca2fd5
4 schema:citation sg:pub.10.1007/bf02572634
5 sg:pub.10.1007/s10468-016-9626-3
6 https://doi.org/10.1006/jabr.1996.6882
7 https://doi.org/10.1016/j.jalgebra.2012.09.018
8 https://doi.org/10.1016/j.jpaa.2006.10.010
9 https://doi.org/10.1080/00927872.2013.780064
10 https://doi.org/10.1080/00927872.2015.1027380
11 https://doi.org/10.1090/memo/0094
12 https://doi.org/10.1112/jlms/jdr014
13 https://doi.org/10.1512/iumj.2008.57.3325
14 https://doi.org/10.1515/9783110199727
15 https://doi.org/10.1515/9783110803662
16 https://doi.org/10.5486/pmd.2017.7689
17 schema:datePublished 2018-10-15
18 schema:datePublishedReg 2018-10-15
19 schema:description In this paper, we explore conditions under which Gorenstein flat modules are Gorenstein projective. We prove that all countably presented strongly Gorenstein flat modules are Gorenstein projective over perfect rings. Moreover, we show that if the base ring R is ∑-pure injective as an R-module, then the class of Gorenstein flat modules coincides with the class of Gorenstein projective modules, and hence all modules have Gorenstein projective covers. And as a corollary, we give a characterization of coherent perfect rings by Gorenstein projective and Gorenstein flat modules.
20 schema:genre research_article
21 schema:inLanguage en
22 schema:isAccessibleForFree false
23 schema:isPartOf sg:journal.1223581
24 schema:name Notes on Gorenstein Flat Modules
25 schema:pagination 1-8
26 schema:productId N3a0b3e27d3694772849466fd3b746b76
27 N484c407a9c794526a841b062820b8e8a
28 N790440bcf7e445a5acd9b18e7d947eec
29 schema:sameAs https://app.dimensions.ai/details/publication/pub.1107645880
30 https://doi.org/10.1007/s41980-018-0135-5
31 schema:sdDatePublished 2019-04-11T02:23
32 schema:sdLicense https://scigraph.springernature.com/explorer/license/
33 schema:sdPublisher N44edadc03a9f45299b1869b07026becc
34 schema:url https://link.springer.com/10.1007%2Fs41980-018-0135-5
35 sgo:license sg:explorer/license/
36 sgo:sdDataset articles
37 rdf:type schema:ScholarlyArticle
38 N36251c3a8a5b4f168176471730015d76 rdf:first sg:person.010315142607.97
39 rdf:rest rdf:nil
40 N3a0b3e27d3694772849466fd3b746b76 schema:name doi
41 schema:value 10.1007/s41980-018-0135-5
42 rdf:type schema:PropertyValue
43 N44edadc03a9f45299b1869b07026becc schema:name Springer Nature - SN SciGraph project
44 rdf:type schema:Organization
45 N484c407a9c794526a841b062820b8e8a schema:name readcube_id
46 schema:value d0753a44a1d742ab75011b636140bea7b85fa2e0aea2416d791169507039a74c
47 rdf:type schema:PropertyValue
48 N790440bcf7e445a5acd9b18e7d947eec schema:name dimensions_id
49 schema:value pub.1107645880
50 rdf:type schema:PropertyValue
51 N9eb780cb225240e1a033aedad7ca2fd5 rdf:first sg:person.013032465253.38
52 rdf:rest N36251c3a8a5b4f168176471730015d76
53 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
54 schema:name Mathematical Sciences
55 rdf:type schema:DefinedTerm
56 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
57 schema:name Pure Mathematics
58 rdf:type schema:DefinedTerm
59 sg:journal.1223581 schema:issn 1017-060X
60 1018-6301
61 schema:name Bulletin of the Iranian Mathematical Society
62 rdf:type schema:Periodical
63 sg:person.010315142607.97 schema:affiliation https://www.grid.ac/institutes/grid.440845.9
64 schema:familyName Yan
65 schema:givenName Xiaoguang
66 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010315142607.97
67 rdf:type schema:Person
68 sg:person.013032465253.38 schema:affiliation https://www.grid.ac/institutes/grid.440657.4
69 schema:familyName Yang
70 schema:givenName Yanjiong
71 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013032465253.38
72 rdf:type schema:Person
73 sg:pub.10.1007/bf02572634 schema:sameAs https://app.dimensions.ai/details/publication/pub.1024840797
74 https://doi.org/10.1007/bf02572634
75 rdf:type schema:CreativeWork
76 sg:pub.10.1007/s10468-016-9626-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021471910
77 https://doi.org/10.1007/s10468-016-9626-3
78 rdf:type schema:CreativeWork
79 https://doi.org/10.1006/jabr.1996.6882 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033692641
80 rdf:type schema:CreativeWork
81 https://doi.org/10.1016/j.jalgebra.2012.09.018 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017221364
82 rdf:type schema:CreativeWork
83 https://doi.org/10.1016/j.jpaa.2006.10.010 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032037039
84 rdf:type schema:CreativeWork
85 https://doi.org/10.1080/00927872.2013.780064 schema:sameAs https://app.dimensions.ai/details/publication/pub.1038640617
86 rdf:type schema:CreativeWork
87 https://doi.org/10.1080/00927872.2015.1027380 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012527708
88 rdf:type schema:CreativeWork
89 https://doi.org/10.1090/memo/0094 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059343143
90 rdf:type schema:CreativeWork
91 https://doi.org/10.1112/jlms/jdr014 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032222200
92 rdf:type schema:CreativeWork
93 https://doi.org/10.1512/iumj.2008.57.3325 schema:sameAs https://app.dimensions.ai/details/publication/pub.1067513769
94 rdf:type schema:CreativeWork
95 https://doi.org/10.1515/9783110199727 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050747020
96 rdf:type schema:CreativeWork
97 https://doi.org/10.1515/9783110803662 schema:sameAs https://app.dimensions.ai/details/publication/pub.1096920672
98 rdf:type schema:CreativeWork
99 https://doi.org/10.5486/pmd.2017.7689 schema:sameAs https://app.dimensions.ai/details/publication/pub.1091320859
100 rdf:type schema:CreativeWork
101 https://www.grid.ac/institutes/grid.440657.4 schema:alternateName Taizhou University
102 schema:name Department of Mathematics, Taizhou University, 225300, Taizhou, China
103 rdf:type schema:Organization
104 https://www.grid.ac/institutes/grid.440845.9 schema:alternateName Nanjing Xiaozhuang University
105 schema:name School of Information Engineering, Nanjing Xiaozhuang University, 211171, Nanjing, China
106 rdf:type schema:Organization
 




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


...