Homomorphisms with Semilocal Endomorphism Rings Between Modules
We study the category Morph(Mod- R ) whose objects are all morphisms between two right R -modules. The behavior of the objects of Mod- R whose endomorphism ring in Morph(Mod- R ) is semilocal is very similar to the behavior of modules with a semilocal endomorphism ring. For instance, direct-sum deco...
Gespeichert in:
| Veröffentlicht in: | Algebras and representation theory 2020-12, Vol.23 (6), p.2237-2256 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 2256 |
|---|---|
| container_issue | 6 |
| container_start_page | 2237 |
| container_title | Algebras and representation theory |
| container_volume | 23 |
| creator | Campanini, Federico El-Deken, Susan F. Facchini, Alberto |
| description | We study the category Morph(Mod-
R
) whose objects are all morphisms between two right
R
-modules. The behavior of the objects of Mod-
R
whose endomorphism ring in Morph(Mod-
R
) is semilocal is very similar to the behavior of modules with a semilocal endomorphism ring. For instance, direct-sum decompositions of a direct sum
⊕
i
=
1
n
M
i
, that is, block-diagonal decompositions, where each object
M
i
of Morph(Mod-
R
) denotes a morphism
μ
M
i
:
M
0
,
i
→
M
1
,
i
and where all the modules
M
j
,
i
have a local endomorphism ring End(
M
j
,
i
), depend on two invariants. This behavior is very similar to that of direct-sum decompositions of serial modules of finite Goldie dimension, which also depend on two invariants (monogeny class and epigeny class). When all the modules
M
j
,
i
are uniserial modules, the direct-sum decompositions (block-diagonal decompositions) of a direct-sum
⊕
i
=
1
n
M
i
depend on four invariants. |
| doi_str_mv | 10.1007/s10468-019-09936-x |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2473816279</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2473816279</sourcerecordid><originalsourceid>FETCH-LOGICAL-c319t-247bb827a051f95d69564a25993d706ba7e9d294e796d825dada4f7a55d7fdc73</originalsourceid><addsrcrecordid>eNp9kFtLAzEQhYMoWKt_wKcFn6O5bJKdJ9HSWqEieAHfQrrJtlv2UpNdWv-90RV9k3mYgTnnzPAhdE7JJSVEXQVKUplhQgETAC7x_gCNqFAMA1FwGGeeSQyMvx2jkxA2hBCQGR2h63lbx_LbdRnqkOzKbp08u7qs2txUybSxv8vkqWxWIbl13c65JnlobV-5cIqOClMFd_bTx-h1Nn2ZzPHi8e5-crPAOafQYZaq5TJjyhBBCxBWgpCpYSL-ahWRS6McWAapUyBtxoQ11qSFMkJYVdhc8TG6GHK3vn3vXej0pu19E0_qmM0zKpmCqGKDKvdtCN4VeuvL2vgPTYn-AqUHUDqC0t-g9D6a-GAKUdysnP-L_sf1CXrNbC8</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2473816279</pqid></control><display><type>article</type><title>Homomorphisms with Semilocal Endomorphism Rings Between Modules</title><source>SpringerLink Journals - AutoHoldings</source><creator>Campanini, Federico ; El-Deken, Susan F. ; Facchini, Alberto</creator><creatorcontrib>Campanini, Federico ; El-Deken, Susan F. ; Facchini, Alberto</creatorcontrib><description>We study the category Morph(Mod-
R
) whose objects are all morphisms between two right
R
-modules. The behavior of the objects of Mod-
R
whose endomorphism ring in Morph(Mod-
R
) is semilocal is very similar to the behavior of modules with a semilocal endomorphism ring. For instance, direct-sum decompositions of a direct sum
⊕
i
=
1
n
M
i
, that is, block-diagonal decompositions, where each object
M
i
of Morph(Mod-
R
) denotes a morphism
μ
M
i
:
M
0
,
i
→
M
1
,
i
and where all the modules
M
j
,
i
have a local endomorphism ring End(
M
j
,
i
), depend on two invariants. This behavior is very similar to that of direct-sum decompositions of serial modules of finite Goldie dimension, which also depend on two invariants (monogeny class and epigeny class). When all the modules
M
j
,
i
are uniserial modules, the direct-sum decompositions (block-diagonal decompositions) of a direct-sum
⊕
i
=
1
n
M
i
depend on four invariants.</description><identifier>ISSN: 1386-923X</identifier><identifier>EISSN: 1572-9079</identifier><identifier>DOI: 10.1007/s10468-019-09936-x</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Associative Rings and Algebras ; Commutative Rings and Algebras ; Decomposition ; Homomorphisms ; Invariants ; Mathematics ; Mathematics and Statistics ; Modules ; Non-associative Rings and Algebras</subject><ispartof>Algebras and representation theory, 2020-12, Vol.23 (6), p.2237-2256</ispartof><rights>Springer Nature B.V. 2019</rights><rights>Springer Nature B.V. 2019.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-247bb827a051f95d69564a25993d706ba7e9d294e796d825dada4f7a55d7fdc73</citedby><cites>FETCH-LOGICAL-c319t-247bb827a051f95d69564a25993d706ba7e9d294e796d825dada4f7a55d7fdc73</cites><orcidid>0000-0002-0144-0193</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10468-019-09936-x$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10468-019-09936-x$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Campanini, Federico</creatorcontrib><creatorcontrib>El-Deken, Susan F.</creatorcontrib><creatorcontrib>Facchini, Alberto</creatorcontrib><title>Homomorphisms with Semilocal Endomorphism Rings Between Modules</title><title>Algebras and representation theory</title><addtitle>Algebr Represent Theor</addtitle><description>We study the category Morph(Mod-
R
) whose objects are all morphisms between two right
R
-modules. The behavior of the objects of Mod-
R
whose endomorphism ring in Morph(Mod-
R
) is semilocal is very similar to the behavior of modules with a semilocal endomorphism ring. For instance, direct-sum decompositions of a direct sum
⊕
i
=
1
n
M
i
, that is, block-diagonal decompositions, where each object
M
i
of Morph(Mod-
R
) denotes a morphism
μ
M
i
:
M
0
,
i
→
M
1
,
i
and where all the modules
M
j
,
i
have a local endomorphism ring End(
M
j
,
i
), depend on two invariants. This behavior is very similar to that of direct-sum decompositions of serial modules of finite Goldie dimension, which also depend on two invariants (monogeny class and epigeny class). When all the modules
M
j
,
i
are uniserial modules, the direct-sum decompositions (block-diagonal decompositions) of a direct-sum
⊕
i
=
1
n
M
i
depend on four invariants.</description><subject>Associative Rings and Algebras</subject><subject>Commutative Rings and Algebras</subject><subject>Decomposition</subject><subject>Homomorphisms</subject><subject>Invariants</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Modules</subject><subject>Non-associative Rings and Algebras</subject><issn>1386-923X</issn><issn>1572-9079</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kFtLAzEQhYMoWKt_wKcFn6O5bJKdJ9HSWqEieAHfQrrJtlv2UpNdWv-90RV9k3mYgTnnzPAhdE7JJSVEXQVKUplhQgETAC7x_gCNqFAMA1FwGGeeSQyMvx2jkxA2hBCQGR2h63lbx_LbdRnqkOzKbp08u7qs2txUybSxv8vkqWxWIbl13c65JnlobV-5cIqOClMFd_bTx-h1Nn2ZzPHi8e5-crPAOafQYZaq5TJjyhBBCxBWgpCpYSL-ahWRS6McWAapUyBtxoQ11qSFMkJYVdhc8TG6GHK3vn3vXej0pu19E0_qmM0zKpmCqGKDKvdtCN4VeuvL2vgPTYn-AqUHUDqC0t-g9D6a-GAKUdysnP-L_sf1CXrNbC8</recordid><startdate>20201201</startdate><enddate>20201201</enddate><creator>Campanini, Federico</creator><creator>El-Deken, Susan F.</creator><creator>Facchini, Alberto</creator><general>Springer Netherlands</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-0144-0193</orcidid></search><sort><creationdate>20201201</creationdate><title>Homomorphisms with Semilocal Endomorphism Rings Between Modules</title><author>Campanini, Federico ; El-Deken, Susan F. ; Facchini, Alberto</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-247bb827a051f95d69564a25993d706ba7e9d294e796d825dada4f7a55d7fdc73</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Associative Rings and Algebras</topic><topic>Commutative Rings and Algebras</topic><topic>Decomposition</topic><topic>Homomorphisms</topic><topic>Invariants</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Modules</topic><topic>Non-associative Rings and Algebras</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Campanini, Federico</creatorcontrib><creatorcontrib>El-Deken, Susan F.</creatorcontrib><creatorcontrib>Facchini, Alberto</creatorcontrib><collection>CrossRef</collection><jtitle>Algebras and representation theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Campanini, Federico</au><au>El-Deken, Susan F.</au><au>Facchini, Alberto</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Homomorphisms with Semilocal Endomorphism Rings Between Modules</atitle><jtitle>Algebras and representation theory</jtitle><stitle>Algebr Represent Theor</stitle><date>2020-12-01</date><risdate>2020</risdate><volume>23</volume><issue>6</issue><spage>2237</spage><epage>2256</epage><pages>2237-2256</pages><issn>1386-923X</issn><eissn>1572-9079</eissn><abstract>We study the category Morph(Mod-
R
) whose objects are all morphisms between two right
R
-modules. The behavior of the objects of Mod-
R
whose endomorphism ring in Morph(Mod-
R
) is semilocal is very similar to the behavior of modules with a semilocal endomorphism ring. For instance, direct-sum decompositions of a direct sum
⊕
i
=
1
n
M
i
, that is, block-diagonal decompositions, where each object
M
i
of Morph(Mod-
R
) denotes a morphism
μ
M
i
:
M
0
,
i
→
M
1
,
i
and where all the modules
M
j
,
i
have a local endomorphism ring End(
M
j
,
i
), depend on two invariants. This behavior is very similar to that of direct-sum decompositions of serial modules of finite Goldie dimension, which also depend on two invariants (monogeny class and epigeny class). When all the modules
M
j
,
i
are uniserial modules, the direct-sum decompositions (block-diagonal decompositions) of a direct-sum
⊕
i
=
1
n
M
i
depend on four invariants.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s10468-019-09936-x</doi><tpages>20</tpages><orcidid>https://orcid.org/0000-0002-0144-0193</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1386-923X |
| ispartof | Algebras and representation theory, 2020-12, Vol.23 (6), p.2237-2256 |
| issn | 1386-923X 1572-9079 |
| language | eng |
| recordid | cdi_proquest_journals_2473816279 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Associative Rings and Algebras Commutative Rings and Algebras Decomposition Homomorphisms Invariants Mathematics Mathematics and Statistics Modules Non-associative Rings and Algebras |
| title | Homomorphisms with Semilocal Endomorphism Rings Between Modules |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-05T03%3A31%3A26IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Homomorphisms%20with%20Semilocal%20Endomorphism%20Rings%20Between%20Modules&rft.jtitle=Algebras%20and%20representation%20theory&rft.au=Campanini,%20Federico&rft.date=2020-12-01&rft.volume=23&rft.issue=6&rft.spage=2237&rft.epage=2256&rft.pages=2237-2256&rft.issn=1386-923X&rft.eissn=1572-9079&rft_id=info:doi/10.1007/s10468-019-09936-x&rft_dat=%3Cproquest_cross%3E2473816279%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2473816279&rft_id=info:pmid/&rfr_iscdi=true |