KFU. Card publication. Lifting of automorphisms of factor modules

KAZAN
FEDERAL UNIVERSITY

- RUS
- 中文
- ES

LIFTING OF AUTOMORPHISMS OF FACTOR MODULES

Form of presentation

Articles in international journals and collections

Year of publication

2018

Язык

английский

Authors, employees of KFU

Abyzov Adel Nailevich, author

Bibliographic description in the original language

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

Annotation

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.

Keywords

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

The name of the journal

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

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

https://repository.kpfu.ru/eng/?p_id=186689&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Abyzov Adel Nailevich	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/eng/?p_id=186689&p_lang=2	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	Articles in international journals and collections	ru_RU