KFU. Card publication. Semisimple-direct-injective modules

KAZAN
FEDERAL UNIVERSITY

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SEMISIMPLE-DIRECT-INJECTIVE MODULES

Form of presentation

Articles in international journals and collections

Year of publication

2021

Язык

английский

Authors, employees of KFU

Abyzov Adel Nailevich, author

Tapkin Danil Tagirzyanovich, author

Bibliographic description in the original language

Abyzov A, Kosan T, Tapkin D.T., Quynh T.C, Semisimple-direct-injective modules//Hacettepe Journal of Mathematics and Statistics. - 2021. - Vol.50, Is.2. - P.516-525.

Annotation

The notion of simple-direct-injective modules which are a generalization of injective modules unifies C2 and C3-modules. In the present paper, we introduce the notion of the semisimple-direct-injective module which gives a unified viewpoint of C2, C3, SSP properties and simple-direct-injective modules. It is proved that a ring R is Artinian serial with the Jacobson radical square zero if and only if every semisimple-direct-injective right R-module has the SSP and, for any family of simple injective right R-modules {Si}I, ⊕ISi is injective. We also show that R is a right Noetherian right V-ring if and only if every right R-module has a semisimple-direct-injective envelope if and only if every right R-module has a semisimple-direct-injective cover.

Keywords

C2-module, C3-module, SSP, Artinian serial ring, V-ring, simple-direct-injective module

The name of the journal

Hacettepe Journal of Mathematics and Statistics

URL

https://www.scopus.com/inward/record.uri?eid=2-s2.0-85105472777&doi=10.15672%2fhujms.730907&partnerID=40&md5=97b348ae5017d494bf030d06897c3ff1

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=253530&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Abyzov Adel Nailevich	ru_RU
dc.contributor.author	Tapkin Danil Tagirzyanovich	ru_RU
dc.date.accessioned	2021-01-01T00:00:00Z	ru_RU
dc.date.available	2021-01-01T00:00:00Z	ru_RU
dc.date.issued	2021	ru_RU
dc.identifier.citation	Abyzov A, Kosan T, Tapkin D.T., Quynh T.C, Semisimple-direct-injective modules//Hacettepe Journal of Mathematics and Statistics. - 2021. - Vol.50, Is.2. - P.516-525.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=253530&p_lang=2	ru_RU
dc.description.abstract	Hacettepe Journal of Mathematics and Statistics	ru_RU
dc.description.abstract	The notion of simple-direct-injective modules which are a generalization of injective modules unifies C2 and C3-modules. In the present paper, we introduce the notion of the semisimple-direct-injective module which gives a unified viewpoint of C2, C3, SSP properties and simple-direct-injective modules. It is proved that a ring R is Artinian serial with the Jacobson radical square zero if and only if every semisimple-direct-injective right R-module has the SSP and, for any family of simple injective right R-modules {Si}I, ⊕ISi is injective. We also show that R is a right Noetherian right V-ring if and only if every right R-module has a semisimple-direct-injective envelope if and only if every right R-module has a semisimple-direct-injective cover.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	C2-module	ru_RU
dc.subject	C3-module	ru_RU
dc.subject	SSP	ru_RU
dc.subject	Artinian serial ring	ru_RU
dc.subject	V-ring	ru_RU
dc.subject	simple-direct-injective module	ru_RU
dc.title	Semisimple-direct-injective modules	ru_RU
dc.type	Articles in international journals and collections	ru_RU