Characterizations of (m,n)-Jordan Derivations and (m,n)-Jordan Derivable Mappings on Some Algebras View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-03

AUTHORS

Guang Yu An, Jun He

ABSTRACT

Let R be a ring, M be a R-bimodule and m, n be two fixed nonnegative integers with m + n ≠ 0. An additive mapping δ from R into M is called an (m, n)-Jordan derivation if (m + n)δ(A2) = 2mAδ(A) + 2nδ(A)A for every A in R. In this paper, we prove that every (m, n)-Jordan derivation with m ≠ n from a C* -algebra into its Banach bimodule is zero. An additive mapping δ from R into M is called a (m, n)-Jordan derivable mapping at W in R if (m + n)δ(AB + BA) = 2mδ(A)B + 2mδ(B)A + 2nAδ(B) + 2nBδ(A) for each A and B in R with AB = BA = W. We prove that if M is a unital A-bimodule with a left (right) separating set generated algebraically by all idempotents in A, then every (m, n)-Jordan derivable mapping at zero from A into M is identical with zero. We also show that if A and B are two unital algebras, M is a faithful unital (A, B)-bimodule and U=[AMNB] is a generalized matrix algebra, then every (m, n)-Jordan derivable mapping at zero from U into itself is equal to zero. More... »

PAGES

1-13

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10114-018-7495-x

DOI

http://dx.doi.org/10.1007/s10114-018-7495-x

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1110506925


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": "Shaanxi University of Science and Technology", 
          "id": "https://www.grid.ac/institutes/grid.454711.2", 
          "name": [
            "Department of Mathematics, Shaanxi University of Science and Technology, 710021, Xi\u2019an, P. R. China"
          ], 
          "type": "Organization"
        }, 
        "familyName": "An", 
        "givenName": "Guang Yu", 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Anhui Polytechnic University", 
          "id": "https://www.grid.ac/institutes/grid.461986.4", 
          "name": [
            "Department of Mathematics and Physics, Anhui Polytechnic University, 241000, Wuhu, P. R. China"
          ], 
          "type": "Organization"
        }, 
        "familyName": "He", 
        "givenName": "Jun", 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1090/s0002-9939-1983-0712641-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1006820324"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1112/jlms/s2-5.3.432", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1014595044"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01351703", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1019374830", 
          "https://doi.org/10.1007/bf01351703"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01351703", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1019374830", 
          "https://doi.org/10.1007/bf01351703"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/s0002-9939-1990-1028284-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1020488871"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/s0002-9939-1957-0095864-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1021198142"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/s0002-9939-1975-0399182-5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1044636320"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00010-007-2872-z", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1049904290", 
          "https://doi.org/10.1007/s00010-007-2872-z"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.jmaa.2003.10.015", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1050618447"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1017/s0004972715001203", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1054775556"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1215/17358787-3599675", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064414560"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.13001/1081-3810.3090", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064879882"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.13001/1081-3810.3090", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064879882"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.13001/1081-3810.3090", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064879882"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.13001/1081-3810.3090", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064879882"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.4064/sm206-2-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1072185205"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2019-03", 
    "datePublishedReg": "2019-03-01", 
    "description": "Let R be a ring, M be a R-bimodule and m, n be two fixed nonnegative integers with m + n \u2260 0. An additive mapping \u03b4 from R into M is called an (m, n)-Jordan derivation if (m + n)\u03b4(A2) = 2mA\u03b4(A) + 2n\u03b4(A)A for every A in R. In this paper, we prove that every (m, n)-Jordan derivation with m \u2260 n from a C* -algebra into its Banach bimodule is zero. An additive mapping \u03b4 from R into M is called a (m, n)-Jordan derivable mapping at W in R if (m + n)\u03b4(AB + BA) = 2m\u03b4(A)B + 2m\u03b4(B)A + 2nA\u03b4(B) + 2nB\u03b4(A) for each A and B in R with AB = BA = W. We prove that if M is a unital A-bimodule with a left (right) separating set generated algebraically by all idempotents in A, then every (m, n)-Jordan derivable mapping at zero from A into M is identical with zero. We also show that if A and B are two unital algebras, M is a faithful unital (A, B)-bimodule and U=[AMNB] is a generalized matrix algebra, then every (m, n)-Jordan derivable mapping at zero from U into itself is equal to zero.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s10114-018-7495-x", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1040372", 
        "issn": [
          "1439-8516", 
          "1439-7617"
        ], 
        "name": "Acta Mathematica Sinica, English Series", 
        "type": "Periodical"
      }
    ], 
    "name": "Characterizations of (m,n)-Jordan Derivations and (m,n)-Jordan Derivable Mappings on Some Algebras", 
    "pagination": "1-13", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "5e2f1985ae166388900abaf0d504c158e31e17abce1e799d115c955a4ff673ec"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s10114-018-7495-x"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1110506925"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s10114-018-7495-x", 
      "https://app.dimensions.ai/details/publication/pub.1110506925"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T08:23", 
    "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/v90/0000000293_0000000293/records_12038_00000000.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://link.springer.com/10.1007%2Fs10114-018-7495-x"
  }
]
 

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/s10114-018-7495-x'

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/s10114-018-7495-x'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s10114-018-7495-x'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s10114-018-7495-x'


 

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

101 TRIPLES      21 PREDICATES      37 URIs      17 LITERALS      5 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s10114-018-7495-x schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N83ce224ce6514027944726e5b78c53cb
4 schema:citation sg:pub.10.1007/bf01351703
5 sg:pub.10.1007/s00010-007-2872-z
6 https://doi.org/10.1016/j.jmaa.2003.10.015
7 https://doi.org/10.1017/s0004972715001203
8 https://doi.org/10.1090/s0002-9939-1957-0095864-2
9 https://doi.org/10.1090/s0002-9939-1975-0399182-5
10 https://doi.org/10.1090/s0002-9939-1983-0712641-2
11 https://doi.org/10.1090/s0002-9939-1990-1028284-3
12 https://doi.org/10.1112/jlms/s2-5.3.432
13 https://doi.org/10.1215/17358787-3599675
14 https://doi.org/10.13001/1081-3810.3090
15 https://doi.org/10.4064/sm206-2-2
16 schema:datePublished 2019-03
17 schema:datePublishedReg 2019-03-01
18 schema:description Let R be a ring, M be a R-bimodule and m, n be two fixed nonnegative integers with m + n ≠ 0. An additive mapping δ from R into M is called an (m, n)-Jordan derivation if (m + n)δ(A2) = 2mAδ(A) + 2nδ(A)A for every A in R. In this paper, we prove that every (m, n)-Jordan derivation with m ≠ n from a C* -algebra into its Banach bimodule is zero. An additive mapping δ from R into M is called a (m, n)-Jordan derivable mapping at W in R if (m + n)δ(AB + BA) = 2mδ(A)B + 2mδ(B)A + 2nAδ(B) + 2nBδ(A) for each A and B in R with AB = BA = W. We prove that if M is a unital A-bimodule with a left (right) separating set generated algebraically by all idempotents in A, then every (m, n)-Jordan derivable mapping at zero from A into M is identical with zero. We also show that if A and B are two unital algebras, M is a faithful unital (A, B)-bimodule and U=[AMNB] is a generalized matrix algebra, then every (m, n)-Jordan derivable mapping at zero from U into itself is equal to zero.
19 schema:genre research_article
20 schema:inLanguage en
21 schema:isAccessibleForFree false
22 schema:isPartOf sg:journal.1040372
23 schema:name Characterizations of (m,n)-Jordan Derivations and (m,n)-Jordan Derivable Mappings on Some Algebras
24 schema:pagination 1-13
25 schema:productId N07237606e38941e68affcc6b76a5d68c
26 N0e6f8f7bd0ea467db90973ef2ecbf181
27 N5840a8f570c14280882ac9ce8d43f20b
28 schema:sameAs https://app.dimensions.ai/details/publication/pub.1110506925
29 https://doi.org/10.1007/s10114-018-7495-x
30 schema:sdDatePublished 2019-04-11T08:23
31 schema:sdLicense https://scigraph.springernature.com/explorer/license/
32 schema:sdPublisher Nd575a1d5ab604c669c7a461434955e9d
33 schema:url https://link.springer.com/10.1007%2Fs10114-018-7495-x
34 sgo:license sg:explorer/license/
35 sgo:sdDataset articles
36 rdf:type schema:ScholarlyArticle
37 N051b07cf6e0b46ef8946d7613ca2f073 schema:affiliation https://www.grid.ac/institutes/grid.454711.2
38 schema:familyName An
39 schema:givenName Guang Yu
40 rdf:type schema:Person
41 N07237606e38941e68affcc6b76a5d68c schema:name readcube_id
42 schema:value 5e2f1985ae166388900abaf0d504c158e31e17abce1e799d115c955a4ff673ec
43 rdf:type schema:PropertyValue
44 N0e6f8f7bd0ea467db90973ef2ecbf181 schema:name doi
45 schema:value 10.1007/s10114-018-7495-x
46 rdf:type schema:PropertyValue
47 N5840a8f570c14280882ac9ce8d43f20b schema:name dimensions_id
48 schema:value pub.1110506925
49 rdf:type schema:PropertyValue
50 N5bf98f600a404915bb21a72dbd7e82e6 rdf:first Nb036011c90784ef0a569cc8dbcff697a
51 rdf:rest rdf:nil
52 N83ce224ce6514027944726e5b78c53cb rdf:first N051b07cf6e0b46ef8946d7613ca2f073
53 rdf:rest N5bf98f600a404915bb21a72dbd7e82e6
54 Nb036011c90784ef0a569cc8dbcff697a schema:affiliation https://www.grid.ac/institutes/grid.461986.4
55 schema:familyName He
56 schema:givenName Jun
57 rdf:type schema:Person
58 Nd575a1d5ab604c669c7a461434955e9d schema:name Springer Nature - SN SciGraph project
59 rdf:type schema:Organization
60 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
61 schema:name Mathematical Sciences
62 rdf:type schema:DefinedTerm
63 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
64 schema:name Pure Mathematics
65 rdf:type schema:DefinedTerm
66 sg:journal.1040372 schema:issn 1439-7617
67 1439-8516
68 schema:name Acta Mathematica Sinica, English Series
69 rdf:type schema:Periodical
70 sg:pub.10.1007/bf01351703 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019374830
71 https://doi.org/10.1007/bf01351703
72 rdf:type schema:CreativeWork
73 sg:pub.10.1007/s00010-007-2872-z schema:sameAs https://app.dimensions.ai/details/publication/pub.1049904290
74 https://doi.org/10.1007/s00010-007-2872-z
75 rdf:type schema:CreativeWork
76 https://doi.org/10.1016/j.jmaa.2003.10.015 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050618447
77 rdf:type schema:CreativeWork
78 https://doi.org/10.1017/s0004972715001203 schema:sameAs https://app.dimensions.ai/details/publication/pub.1054775556
79 rdf:type schema:CreativeWork
80 https://doi.org/10.1090/s0002-9939-1957-0095864-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021198142
81 rdf:type schema:CreativeWork
82 https://doi.org/10.1090/s0002-9939-1975-0399182-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044636320
83 rdf:type schema:CreativeWork
84 https://doi.org/10.1090/s0002-9939-1983-0712641-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006820324
85 rdf:type schema:CreativeWork
86 https://doi.org/10.1090/s0002-9939-1990-1028284-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020488871
87 rdf:type schema:CreativeWork
88 https://doi.org/10.1112/jlms/s2-5.3.432 schema:sameAs https://app.dimensions.ai/details/publication/pub.1014595044
89 rdf:type schema:CreativeWork
90 https://doi.org/10.1215/17358787-3599675 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064414560
91 rdf:type schema:CreativeWork
92 https://doi.org/10.13001/1081-3810.3090 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064879882
93 rdf:type schema:CreativeWork
94 https://doi.org/10.4064/sm206-2-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072185205
95 rdf:type schema:CreativeWork
96 https://www.grid.ac/institutes/grid.454711.2 schema:alternateName Shaanxi University of Science and Technology
97 schema:name Department of Mathematics, Shaanxi University of Science and Technology, 710021, Xi’an, P. R. China
98 rdf:type schema:Organization
99 https://www.grid.ac/institutes/grid.461986.4 schema:alternateName Anhui Polytechnic University
100 schema:name Department of Mathematics and Physics, Anhui Polytechnic University, 241000, Wuhu, P. R. China
101 rdf:type schema:Organization
 




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


...