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Rings Characterized via Some Classes of Almost-Injective Modules

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dc.contributor.author Quynh T.C.
dc.contributor.author Abyzov A.
dc.contributor.author Dan P.
dc.contributor.author Van Thuyet L.
dc.date.accessioned 2021-02-25T20:36:27Z
dc.date.available 2021-02-25T20:36:27Z
dc.date.issued 2020
dc.identifier.issn 1018-6301
dc.identifier.uri https://dspace.kpfu.ru/xmlui/handle/net/162018
dc.description.abstract © 2020, Iranian Mathematical Society. In this paper, we study rings with the property that every cyclic module is almost-injective (CAI). It is shown that R is an Artinian serial ring with J(R) 2= 0 if and only if R is a right CAI-ring with the finitely generated right socle (or I-finite) if and only if every semisimple right R-module is almost injective, RR is almost injective and has finitely generated right socle. Especially, R is a two-sided CAI-ring if and only if every (right and left) R-module is almost injective. From this, we have the decomposition of a CAI-ring via an SV-ring for which Loewy (R) ≤ 2 and an Artinian serial ring whose squared Jacobson radical vanishes. We also characterize a Noetherian right almost V-ring via the ring for which every semisimple right R-module is almost injective.
dc.relation.ispartofseries Bulletin of the Iranian Mathematical Society
dc.subject Almost V-ring
dc.subject Almost-injective module
dc.subject CAI-ring
dc.subject V-ring
dc.title Rings Characterized via Some Classes of Almost-Injective Modules
dc.type Article
dc.collection Публикации сотрудников КФУ
dc.source.id SCOPUS10186301-2020-SID85094925774

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  • Публикации сотрудников КФУ Scopus [22633]
    Коллекция содержит публикации сотрудников Казанского федерального (до 2010 года Казанского государственного) университета, проиндексированные в БД Scopus, начиная с 1970г.

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