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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 | |
dc.subject | Nilpotentcoinvariant module | |
dc.title | Modules which are invariant under nilpotents of their envelopes and covers | |
dc.type | Article | |
dc.collection | Публикации сотрудников КФУ | |
dc.source.id | SCOPUS02194988-2020-SID85095447890 |