Lie triple derivations of unital algebras with idempotents

Let be a unital algebra with a nontrivial idempotent over a unital commutative ring . We show that under suitable assumptions, every Lie triple derivation on is of the form , where is a derivation of , is a singular Jordan derivation of and is a linear mapping from to its centre that vanishes on . A...

Full description

Saved in:
Bibliographic Details
Published inLinear & multilinear algebra Vol. 63; no. 1; pp. 141 - 165
Main Author Benkovic, Dominik
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 02.01.2015
Taylor & Francis Ltd
Subjects
Algebra
Derivation
Jordan derivation
Lie derivation
Lie triple derivation
Mapping
Mathematical analysis
Matrix algebra
Rings (mathematics)
triangular algebra
unital algebra
Online AccessGet full text

Cover

Abstract Let be a unital algebra with a nontrivial idempotent over a unital commutative ring . We show that under suitable assumptions, every Lie triple derivation on is of the form , where is a derivation of , is a singular Jordan derivation of and is a linear mapping from to its centre that vanishes on . As an application, we characterize Lie triple derivations and Lie derivations on triangular algebras and on matrix algebras.
AbstractList Let [Image omitted.] be a unital algebra with a nontrivial idempotent [Image omitted.] over a unital commutative ring [Image omitted.]. We show that under suitable assumptions, every Lie triple derivation [Image omitted.] on [Image omitted.] is of the form [Image omitted.], where [Image omitted.] is a derivation of [Image omitted.], [Image omitted.] is a singular Jordan derivation of [Image omitted.] and [Image omitted.] is a linear mapping from [Image omitted.] to its centre [Image omitted.] that vanishes on [Image omitted.]. As an application, we characterize Lie triple derivations and Lie derivations on triangular algebras and on matrix algebras.
Let [Formula omitted.] be a unital algebra with a nontrivial idempotent [Formula omitted.] over a unital commutative ring [Formula omitted.] . We show that under suitable assumptions, every Lie triple derivation [Formula omitted.] on [Formula omitted.] is of the form [Formula omitted.] , where [Formula omitted.] is a derivation of [Formula omitted.] , [Formula omitted.] is a singular Jordan derivation of [Formula omitted.] and [Formula omitted.] is a linear mapping from [Formula omitted.] to its centre [Formula omitted.] that vanishes on [Formula omitted.] . As an application, we characterize Lie triple derivations and Lie derivations on triangular algebras and on matrix algebras.
Let be a unital algebra with a nontrivial idempotent over a unital commutative ring . We show that under suitable assumptions, every Lie triple derivation on is of the form , where is a derivation of , is a singular Jordan derivation of and is a linear mapping from to its centre that vanishes on . As an application, we characterize Lie triple derivations and Lie derivations on triangular algebras and on matrix algebras.
Author Benkovič, Dominik
Author_xml – sequence: 1
  givenname: Dominik
  surname: Benkovic
  fullname: Benkovic, Dominik
BookMark eNp9kDtPwzAUhS0EEm3hHzBEYmFJuX4kcVgQqnhJlRhgt5zEBleJHWyHqv-eRIGFgeme4TtHV98SHVtnFUIXGNYYOFwDBT6GYk0A0zXPMAE4Qguc5TTNMC2P0WJC0ok5RcsQdgDAMM0W6GZrVBK96VuVNMqbLxmNsyFxOhmsibJNZPuuKi9DsjfxIzGN6noXlY3hDJ1o2QZ1_nNX6PXh_m3zlG5fHp83d9u0ZpTHlOisZAVUJas4zfOyIIRTrDGnRFJec0lAa80aTKHgNbCqaggua8pUhfOGrtDVvNp79zmoEEVnQq3aVlrlhiBwzgghkBXZiF7-QXdu8Hb8baQw5-NsiUeKzVTtXQheadF700l_EBjEpFP86hSTTjHrHGu3c81Y7Xwn9863jYjy0DqvvbS1CYL-u_ANnLB7Ng
CitedBy_id crossref_primary_10_1007_s41980_021_00618_3
crossref_primary_10_1080_03081087_2015_1063578
crossref_primary_10_1007_s11253_021_01941_y
crossref_primary_10_1142_S0219498823500597
crossref_primary_10_1080_03081087_2019_1570068
crossref_primary_10_1216_rmj_2020_50_163
crossref_primary_10_2989_16073606_2021_2013972
crossref_primary_10_3934_math_2023747
crossref_primary_10_1007_s11401_018_0098_0
crossref_primary_10_1142_S1005386718000329
crossref_primary_10_2298_FIL2330323A
crossref_primary_10_18514_MMN_2024_4413
crossref_primary_10_1007_s10998_022_00459_5
crossref_primary_10_1007_s13370_019_00733_9
crossref_primary_10_1080_00927872_2022_2057522
crossref_primary_10_1080_00927872_2020_1789160
crossref_primary_10_1080_00927872_2016_1172633
crossref_primary_10_37863_umzh_v73i4_838
crossref_primary_10_1007_s41980_020_00493_4
crossref_primary_10_1080_00927872_2023_2263082
crossref_primary_10_1142_S0219498822501651
crossref_primary_10_12677_aam_2024_135189
crossref_primary_10_1080_00927872_2016_1277388
crossref_primary_10_3390_axioms11070328
crossref_primary_10_3934_math_2022422
crossref_primary_10_1007_s41980_021_00609_4
crossref_primary_10_1007_s13226_024_00570_y
crossref_primary_10_1007_s40574_018_0177_x
crossref_primary_10_3103_S1066369X2109005X
crossref_primary_10_1080_00927872_2017_1383999
crossref_primary_10_3934_math_2022771
crossref_primary_10_1007_s41980_019_00348_7
crossref_primary_10_1007_s00010_018_0634_8
crossref_primary_10_1080_00927872_2023_2269579
crossref_primary_10_1515_gmj_2023_2030
crossref_primary_10_1007_s13398_022_01233_5
crossref_primary_10_1080_03081087_2022_2104788
crossref_primary_10_1007_s43037_023_00282_1
crossref_primary_10_1080_00927872_2024_2360174
Cites_doi 10.1016/j.laa.2011.02.048
10.2307/2154392
10.1016/j.laa.2012.01.022
10.1002/mana.200410520
10.1016/j.laa.2012.06.013
10.1016/j.laa.2005.12.003
10.1016/j.laa.2009.12.042
10.1090/S0002-9939-1978-0487480-9
10.1016/j.laa.2012.04.015
10.1080/0308108031000096993
10.1016/j.laa.2005.02.004
10.1080/03081087.2010.499538
10.7153/oam-07-23
10.1016/j.laa.2012.10.052
10.1016/j.laa.2008.06.032
10.1016/j.laa.2010.08.002
10.1016/j.laa.2011.08.024
10.1080/03081087.2011.652109
10.1090/S0002-9947-1950-0038335-X
10.1016/j.laa.2012.06.009
10.1112/S0024610700001642
10.1016/j.laa.2011.07.014
10.1090/S0002-9939-1957-0095863-0
ContentType Journal Article
Copyright 2014 Taylor & Francis 2014
2014 Taylor & Francis
Copyright_xml – notice: 2014 Taylor & Francis 2014
– notice: 2014 Taylor & Francis
DBID AAYXX
CITATION
7SC
8FD
JQ2
L7M
L~C
L~D
DOI 10.1080/03081087.2013.851200
DatabaseName CrossRef
Computer and Information Systems Abstracts
Technology Research Database
ProQuest Computer Science Collection
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
DatabaseTitle CrossRef
Computer and Information Systems Abstracts
Technology Research Database
Computer and Information Systems Abstracts – Academic
Advanced Technologies Database with Aerospace
ProQuest Computer Science Collection
Computer and Information Systems Abstracts Professional
DatabaseTitleList Computer and Information Systems Abstracts
Computer and Information Systems Abstracts
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EISSN 1563-5139
EndPage 165
ExternalDocumentID 3476735541
10_1080_03081087_2013_851200
851200
Genre Articles
Feature
GroupedDBID -~X
.7F
.QJ
0BK
0R~
29L
30N
4.4
5GY
5VS
AAAVI
AAENE
AAJMT
AALDU
AAMIU
AAPUL
AAQRR
ABBKH
ABCCY
ABFIM
ABHAV
ABJVF
ABLIJ
ABPEM
ABPTK
ABQHQ
ABTAI
ABXUL
ACGEJ
ACGFS
ACIWK
ACTIO
ADCVX
ADGTB
ADIYS
ADXPE
AEGYZ
AEISY
AENEX
AEOZL
AEPSL
AEYOC
AFKVX
AFOLD
AFWLO
AGDLA
AGMYJ
AHDLD
AIJEM
AIRXU
AJWEG
AKBVH
AKOOK
ALMA_UNASSIGNED_HOLDINGS
ALQZU
AQRUH
AVBZW
AWYRJ
BLEHA
CCCUG
CE4
CS3
DGEBU
DKSSO
DU5
EBS
EJD
E~A
E~B
FUNRP
FVPDL
GTTXZ
H13
HF~
HZ~
H~P
IPNFZ
J.P
KYCEM
M4Z
NA5
NY~
O9-
P2P
PQEST
PQQKQ
RIG
RNANH
ROSJB
RTWRZ
S-T
SNACF
TEJ
TFL
TFT
TFW
TN5
TTHFI
TWF
UPT
UT5
UU3
V1K
YQT
ZGOLN
~S~
AAYXX
ABJNI
ABPAQ
ABXYU
AHDZW
CITATION
TBQAZ
TDBHL
TUROJ
7SC
8FD
JQ2
L7M
L~C
L~D
ID FETCH-LOGICAL-c438t-2f59470b94b83669722831f1832a38c8a20fff4d13078c04bbd219c34eb16d3
ISSN 0308-1087
IngestDate Thu Aug 15 23:20:28 EDT 2024
Fri Sep 13 06:19:48 EDT 2024
Fri Aug 23 03:03:28 EDT 2024
Tue Jun 13 19:28:17 EDT 2023
IsPeerReviewed true
IsScholarly true
Issue 1
Language English
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-c438t-2f59470b94b83669722831f1832a38c8a20fff4d13078c04bbd219c34eb16d3
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
PQID 1618821991
PQPubID 186326
PageCount 25
ParticipantIDs informaworld_taylorfrancis_310_1080_03081087_2013_851200
proquest_miscellaneous_1642220575
proquest_journals_1618821991
crossref_primary_10_1080_03081087_2013_851200
PublicationCentury 2000
PublicationDate 2015-01-02
PublicationDateYYYYMMDD 2015-01-02
PublicationDate_xml – month: 01
  year: 2015
  text: 2015-01-02
  day: 02
PublicationDecade 2010
PublicationPlace Abingdon
PublicationPlace_xml – name: Abingdon
PublicationTitle Linear & multilinear algebra
PublicationYear 2015
Publisher Taylor & Francis
Taylor & Francis Ltd
Publisher_xml – name: Taylor & Francis
– name: Taylor & Francis Ltd
References CIT0010
CIT0021
CIT0020
CIT0001
CIT0012
CIT0023
CIT0011
CIT0022
Li Y-B (CIT0013) 2011; 22
CIT0003
CIT0014
CIT0002
CIT0024
CIT0005
CIT0016
CIT0004
CIT0015
CIT0007
CIT0018
CIT0006
CIT0017
CIT0009
CIT0008
CIT0019
References_xml – ident: CIT0016
  doi: 10.1016/j.laa.2011.02.048
– ident: CIT0001
  doi: 10.2307/2154392
– ident: CIT0018
  doi: 10.1016/j.laa.2012.01.022
– ident: CIT0004
  doi: 10.1002/mana.200410520
– ident: CIT0012
  doi: 10.1016/j.laa.2012.06.013
– ident: CIT0008
  doi: 10.1016/j.laa.2005.12.003
– ident: CIT0017
  doi: 10.1016/j.laa.2009.12.042
– ident: CIT0005
  doi: 10.1090/S0002-9939-1978-0487480-9
– ident: CIT0019
  doi: 10.1016/j.laa.2012.04.015
– volume: 22
  start-page: 743
  year: 2011
  ident: CIT0013
  publication-title: Elect. J. Linear Algebra
  contributor:
    fullname: Li Y-B
– ident: CIT0015
  doi: 10.1080/0308108031000096993
– ident: CIT0003
  doi: 10.1016/j.laa.2005.02.004
– ident: CIT0007
  doi: 10.1080/03081087.2010.499538
– ident: CIT0010
  doi: 10.7153/oam-07-23
– ident: CIT0020
  doi: 10.1016/j.laa.2012.10.052
– ident: CIT0006
  doi: 10.1016/j.laa.2008.06.032
– ident: CIT0014
  doi: 10.1016/j.laa.2010.08.002
– ident: CIT0023
  doi: 10.1016/j.laa.2011.08.024
– ident: CIT0002
  doi: 10.1080/03081087.2011.652109
– ident: CIT0024
  doi: 10.1090/S0002-9947-1950-0038335-X
– ident: CIT0009
  doi: 10.1016/j.laa.2012.06.009
– ident: CIT0022
  doi: 10.1112/S0024610700001642
– ident: CIT0011
  doi: 10.1016/j.laa.2011.07.014
– ident: CIT0021
  doi: 10.1090/S0002-9939-1957-0095863-0
SSID ssj0004135
Score 2.2689757
Snippet Let be a unital algebra with a nontrivial idempotent over a unital commutative ring . We show that under suitable assumptions, every Lie triple derivation on...
Let [Formula omitted.] be a unital algebra with a nontrivial idempotent [Formula omitted.] over a unital commutative ring [Formula omitted.] . We show that...
Let [Image omitted.] be a unital algebra with a nontrivial idempotent [Image omitted.] over a unital commutative ring [Image omitted.]. We show that under...
SourceID proquest
crossref
informaworld
SourceType Aggregation Database
Publisher
StartPage 141
SubjectTerms Algebra
Derivation
Jordan derivation
Lie derivation
Lie triple derivation
Mapping
Mathematical analysis
Matrix algebra
Rings (mathematics)
triangular algebra
unital algebra
Title Lie triple derivations of unital algebras with idempotents
URI https://www.tandfonline.com/doi/abs/10.1080/03081087.2013.851200
https://www.proquest.com/docview/1618821991/abstract/
https://search.proquest.com/docview/1642220575
Volume 63
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3NT9swFLc2uLADgsG0joI8aTcU1MSO43CrYFOF6C4DDe0S2YktIaYE0bQH_nrei500FISAS9SmiZ36Pb-vvPd7hPxQKrYjrUSgBQcHhRUgB00RB8lIJ0rYPNc5xiGnv8Xkkp9dxVfLRpdNdUmtj_L7Z-tK3kNVOAd0xSrZN1C2GxROwGegLxyBwnB8FY3Pr81hfdfkAxYw32KZ1jYvsRnIITbxAHfYl7BhL9jbqm7Rm7oyaDA0lWuz0aQX_nff_b2dv27Km2px3Rifp870RliSm37YIIybsEE_ksgaXFev7YyXfoIFcejQhVrx6OVPnw2crAsdYpVXm6Fr-fBEIvsURpgNJ8NcOnYEVp7DJ10BwF5RTF26YNjimPpRMhwlc6N8JOtRksbgd6-PJ6f__i6LYn131fZ_tnWTCKz-zNM8skseodY-0dKN6XGxRTa9z0DHjgG2yQdTfiafph3g7myHHAMrUMcKtMcKtLLUsQJtWYEiK9AeK-ySP79-XpxMAt8WI8g5k3UQ2TjlsJdSriUTIk0QwSi0KJsVk7lU0chaywuwThKZj7jWBailnHFQy6JgX8haWZXmK6FKaKFShU5qwk3ENZMaLFCplZZwaTIgQbsk2a3DPsleIsWAyP66ZXUTc7KuQUzGXr512K5x5jfYLMNeDjLC3LwB-d79DOIP32mp0lRzvAZjmOh0fHvj0-6RjeW-GJK1-m5u9sHArPWBZ6UHFKxwSw
link.rule.ids 315,786,790,27957,27958,60241,61030
linkProvider Library Specific Holdings
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV07T8MwED7xGICBN6JQwEisKWnsOC4bQqACbRdAYrPsJJYQUlqRdOHXc5cHUBAMsEVynnf2Pb6cvwM4MSZ0vjXSs1JggsITtINpEnqRbyMjXRzbmHDI4Uj2H8TNY9hUE-Z1WSXl0K4iiihtNS1uAqObkrhT4ljBg4gqs3gHYwZU9TwsSvQ3tDa5P_rYGln32OQli6mKmt1zP9xlxjvNcJd-s9WlA7paA9u8elV38tyZFrYTv35hdfzXt63Dah2esvNqPm3AXJptwsrwnds134KzwVPKihcC6FmC87fCdHM2dmyaUQsSRq1DMAnPGYG8jDrQTsYFFWxsw93V5f1F36s7MHix4KrwAhf2BKqtJ6ziUvYiIsvpOjIDhqtYmcB3zokEHWGkYl9Ym6AFjLlADyATvgML2ThLd4EZaaXpGcqHIpEGwnJlMdhR1liFp0Yt8Bq560lFs6G7DXtpLRFNEtGVRFqgPitHFyW84apeJJr_fmm7UaSu12uuqW2ACqgMrAXH78O40uj3icnS8ZTOIbiM4tu9vz_9CJb698OBHlyPbvdhGUfCEtAJ2rBQvEzTAwxxCntYTuI3elDs_Q
linkToPdf http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3dS8MwED90guiD3-J0agRfO7smTTPfRB1TtyGosLeQtA2I0I6te_GvN9ePuSn6oG-F9PMuudxd734_gHOlfONqxR3NmQ1QaGTtYBz5TuDqQHEThjrEPGR_wLsv7H7oD-e6-LGsEmNoUwBF5LYaF_coMlVF3AVCrNiDAAuzaNO6DFbTy7DCkTELmzjcwWdnZEmxSXMQUxFUzXM_3GVhc1qALv1mqvP9p7MJqnrzouzkrTnNdDN8_wLq-J9P24KN0jklV8Vs2oalONmB9f4M2XWyC5e915hkY0zPk8jO3iKjOyGpIdMECUgIEofYEHxCMMVLkH92lGZYrrEHT53b5-uuU_IvOCGjInM847eZVVqbaUE5bwcIldMyaAQUFaFQnmuMYZHdBgMRukzryNq_kDJr_3lE96GWpEl8AERxzVVbYTQUsNhjmgptXR2hlRb21KAOTiV2OSpANmSrwi4tJSJRIrKQSB3EvG5klic3TMFEIunvlzYqPcpytU4kkgYID4vA6nA2G7brDH-eqCROp3gOJsvQuz38-9NPYfXxpiN7d4OHI1izA36ezfEaUMvG0_jY-jeZPsmn8Aes7euq
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Lie+triple+derivations+of+unital+algebras+with+idempotents&rft.jtitle=Linear+%26+multilinear+algebra&rft.au=Benkovi%C4%8D%2C+Dominik&rft.date=2015-01-02&rft.issn=0308-1087&rft.eissn=1563-5139&rft.volume=63&rft.issue=1&rft.spage=141&rft.epage=165&rft_id=info:doi/10.1080%2F03081087.2013.851200&rft.externalDBID=n%2Fa&rft.externalDocID=10_1080_03081087_2013_851200
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0308-1087&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0308-1087&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0308-1087&client=summon