KFU. Card publication. CS-Rickart modules

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CS-RICKART MODULES

Form of presentation

Articles in Russian journals and collections

Year of publication

2014

Язык

русский

Authors, employees of KFU

Abyzov Adel Nailevich, author

Authors, postgraduates KFU

Chan Khoay Ngok Nyan, postgraduate kfu

Bibliographic description in the original language

A. N. Abyzov, T. H. N. Nhan, CS-Rickart modules, Lobachevskii Journal of Mathematics, 2014, Vol. 35, No. 4, pp. 316–325.

Annotation

In this paper, we introduce and study the concept of CS-Rickart modules, that is a module analogue of the concept of ACS rings. A ring R is called a right weakly semihereditary ring if every its finitly generated right ideal is of the form P . S, where PR is a projective module and SR is a singular module. We describe the ring R over which Matn(R) is a right ACS ring for any n Ѓё N. We show that every finitely generated projective right R-module will to be a CS-Rickart module, is precisely when R is a right weakly semihereditary ring. Also, we prove that if R is a right weakly semihereditary ring, then every finitely generated submodule of a projective right R-module has the form P1 . . . . . Pn . S, where every P1, . . . , Pn is a projective module which is isomorphic to a submodule of RR, and SR is a singular module. As corollaries we obtain some well-known properties of Rickart modules and semihereditary rings.

Keywords

CS-Rickart modules, Rickart modules, ACS rings, semihereditary rings.

The name of the journal

Lobachevskii Journal of Math.

URL

http://link.springer.com/journal/volumesAndIssues/12202

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

https://repository.kpfu.ru/eng/?p_id=89670&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Abyzov Adel Nailevich	ru_RU
dc.contributor.author	Chan Khoay Ngok Nyan	ru_RU
dc.date.accessioned	2014-01-01T00:00:00Z	ru_RU
dc.date.available	2014-01-01T00:00:00Z	ru_RU
dc.date.issued	2014	ru_RU
dc.identifier.citation	A. N. Abyzov, T. H. N. Nhan, CS-Rickart modules, Lobachevskii Journal of Mathematics, 2014, Vol. 35, No. 4, pp. 316–325.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=89670&p_lang=2	ru_RU
dc.description.abstract	Lobachevskii Journal of Math.	ru_RU
dc.description.abstract	In this paper, we introduce and study the concept of CS-Rickart modules, that is a module analogue of the concept of ACS rings. A ring R is called a right weakly semihereditary ring if every its finitly generated right ideal is of the form P . S, where PR is a projective module and SR is a singular module. We describe the ring R over which Matn(R) is a right ACS ring for any n Ѓё N. We show that every finitely generated projective right R-module will to be a CS-Rickart module, is precisely when R is a right weakly semihereditary ring. Also, we prove that if R is a right weakly semihereditary ring, then every finitely generated submodule of a projective right R-module has the form P1 . . . . . Pn . S, where every P1, . . . , Pn is a projective module which is isomorphic to a submodule of RR, and SR is a singular module. As corollaries we obtain some well-known properties of Rickart modules and semihereditary rings.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	CS-Rickart modules	ru_RU
dc.subject	Rickart modules	ru_RU
dc.subject	ACS rings	ru_RU
dc.subject	semihereditary rings.	ru_RU
dc.title	CS-Rickart modules	ru_RU
dc.type	Articles in Russian journals and collections	ru_RU