Form of presentation | Articles in international journals and collections |
Year of publication | 2018 |
Язык | английский |
|
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 ![](https://shelly.kpfu.ru/pdf/picture/arrow_black_right.gif) |
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 |
|