dc.contributor.author |
Quynh T.C. |
|
dc.contributor.author |
Abyzov A. |
|
dc.contributor.author |
Tai D.D. |
|
dc.date.accessioned |
2021-02-25T20:34:40Z |
|
dc.date.available |
2021-02-25T20:34:40Z |
|
dc.date.issued |
2020 |
|
dc.identifier.issn |
0219-4988 |
|
dc.identifier.uri |
https://dspace.kpfu.ru/xmlui/handle/net/161809 |
|
dc.description.abstract |
© 2020 World Scientific Publishing Co. Pte Ltd. All rights reserved. A module is called nilpotent-invariant if it is invariant under any nilpotent endomorphism of its injective envelope [M. T. Kosan and T. C. Quynh, Nilpotent-invaraint modules and rings, Comm. Algebra 45 (2017) 2775-2782]. In this paper, we continue the study of nilpotent-invariant modules and analyze their relationship to (quasi-)injective modules. It is proved that a right module M over a semiprimary ring is nilpotentinvariant iff all nilpotent endomorphisms of submodules of M extend to nilpotent endomorphisms of M. It is also shown that a right module M over a prime right Goldie ring with dim(M/Z(M)) > 1 is nilpotent-invariant iff it is injective. We also study nilpotent-coinvariant modules that are the dual notation of nilpotent-invariant modules. It is proved that if M is a finitely generated nilpotent-coinvariant right module with M/J(M) square-full, then M is quasi-projective. Some characterizations and structures of nilpotent-coinvariant modules are considered. |
|
dc.relation.ispartofseries |
Journal of Algebra and its Applications |
|
dc.subject |
Automorphism-coinvariant module |
|
dc.subject |
Nilpotent-invariant module |
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dc.subject |
Nilpotentcoinvariant module |
|
dc.title |
Modules which are invariant under nilpotents of their envelopes and covers |
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dc.type |
Article |
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dc.collection |
Публикации сотрудников КФУ |
|
dc.source.id |
SCOPUS02194988-2020-SID85095447890 |
|