КФУ. Карточка публикации. Lifting of automorphisms of factor modules

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LIFTING OF AUTOMORPHISMS OF FACTOR MODULES

Форма представления

Статьи в зарубежных журналах и сборниках

Год публикации

2018

Язык

английский

Авторы, сотрудники КФУ

Абызов Адель Наилевич, автор

Библиографическое описание на языке оригинала

Abyzov A.N, Truong C.Q., Lifting of automorphisms of factor modules//Communications in Algebra. - 2018. - Vol.46, Is.11. - P.5073-5082.

Аннотация

This paper introduces the notion of dual of automorphism extendable modules. A module M is called automorphism-extendable if for every submodule N of M, every automorphism of N can be extended to an endomorphism of M. We call a module M a dual automorphism-extendable module if whenever K is a submodule of M, then every automorphism ν:M∕K → M∕K lifts to an endomorphism 𝜃 of M. In this paper we give various examples of dual automorphism-extendable modules and study their properties. In particular, we prove that every dual automorphism-extendable module is a D3-module. It is shown that over a right artinian ring R, an R-module M=⊕IMi with hollow modules Mi is dual automorphism-extendable if and only if M is quasi-projective.

Ключевые слова

Artinian ring, dual automorphism-extendable module, dual automorphism-invariant module, perfect ring, quasi-projective module

Название журнала

COMMUNICATIONS IN ALGEBRA

URL

https://www.scopus.com/inward/record.uri?eid=2-s2.0-85053494009&doi=10.1080%2f00927872.2018.1461884&partnerID=40&md5=dbfbedf24d5512fb9219ca4bb4831bbe

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https://repository.kpfu.ru/?p_id=186689

Полная запись метаданных

Поле DC	Значение	Язык
dc.contributor.author	Абызов Адель Наилевич	ru_RU
dc.date.accessioned	2018-01-01T00:00:00Z	ru_RU
dc.date.available	2018-01-01T00:00:00Z	ru_RU
dc.date.issued	2018	ru_RU
dc.identifier.citation	Abyzov A.N, Truong C.Q., Lifting of automorphisms of factor modules//Communications in Algebra. - 2018. - Vol.46, Is.11. - P.5073-5082.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/?p_id=186689	ru_RU
dc.description.abstract	COMMUNICATIONS IN ALGEBRA	ru_RU
dc.description.abstract	This paper introduces the notion of dual of automorphism extendable modules. A module M is called automorphism-extendable if for every submodule N of M, every automorphism of N can be extended to an endomorphism of M. We call a module M a dual automorphism-extendable module if whenever K is a submodule of M, then every automorphism ν:M∕K → M∕K lifts to an endomorphism 𝜃 of M. In this paper we give various examples of dual automorphism-extendable modules and study their properties. In particular, we prove that every dual automorphism-extendable module is a D3-module. It is shown that over a right artinian ring R, an R-module M=⊕IMi with hollow modules Mi is dual automorphism-extendable if and only if M is quasi-projective.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	Artinian ring	ru_RU
dc.subject	dual automorphism-extendable module	ru_RU
dc.subject	dual automorphism-invariant module	ru_RU
dc.subject	perfect ring	ru_RU
dc.subject	quasi-projective module	ru_RU
dc.title	Lifting of automorphisms of factor modules	ru_RU
dc.type	Статьи в зарубежных журналах и сборниках	ru_RU