КФУ. Карточка публикации. Semisimple-direct-injective modules

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SEMISIMPLE-DIRECT-INJECTIVE MODULES

Форма представления

Статьи в зарубежных журналах и сборниках

Год публикации

2021

Язык

английский

Авторы, сотрудники КФУ

Абызов Адель Наилевич, автор

Тапкин Даниль Тагирзянович, автор

Библиографическое описание на языке оригинала

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.

Аннотация

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.

Ключевые слова

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

Название журнала

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

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https://repository.kpfu.ru/?p_id=253530

Полная запись метаданных

Поле DC	Значение	Язык
dc.contributor.author	Абызов Адель Наилевич	ru_RU
dc.contributor.author	Тапкин Даниль Тагирзянович	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/?p_id=253530	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	Статьи в зарубежных журналах и сборниках	ru_RU