dc.contributor.author |
Koşan M. |
|
dc.contributor.author |
Quynh T. |
|
dc.date.accessioned |
2018-09-19T21:48:35Z |
|
dc.date.available |
2018-09-19T21:48:35Z |
|
dc.date.issued |
2016 |
|
dc.identifier.issn |
1793-5571 |
|
dc.identifier.uri |
https://dspace.kpfu.ru/xmlui/handle/net/144362 |
|
dc.description.abstract |
© 2017 World Scientific Publishing CompanyThe aim of the present article is to investigate the structure of rings (Formula presented.) satisfying the condition: for any family (Formula presented.) of simple right (Formula presented.)-modules, every essential extension of (Formula presented.) is a direct sum of lifting modules, where (Formula presented.) denotes the injective hull. We show that every essential extension of (Formula presented.) is a direct sum of lifting modules if and only if (Formula presented.) is right Noetherian and (Formula presented.) is hollow. Assume that (Formula presented.) is an injective right (Formula presented.)-module with essential socle. We also prove that if every essential extension of (Formula presented.) is a direct sum of lifting modules, then (Formula presented.) is (Formula presented.)-injective. As a consequence of this observation, we show that (Formula presented.) is a right V-ring and every essential extension of (Formula presented.) is a direct sum of lifting modules for all simple modules (Formula presented.) if and only if (Formula presented.) is a right (Formula presented.)-V-ring. |
|
dc.relation.ispartofseries |
Asian-European Journal of Mathematics |
|
dc.subject |
(Formula presented.)-injective module |
|
dc.subject |
(Formula presented.)-lifting module |
|
dc.subject |
(Formula presented.)-V-ring |
|
dc.subject |
H-ring |
|
dc.subject |
Hollow module |
|
dc.subject |
lifting module |
|
dc.subject |
Noetherian ring |
|
dc.subject |
QF-ring |
|
dc.title |
On infinite direct sums of lifting modules |
|
dc.type |
Article in Press |
|
dc.collection |
Публикации сотрудников КФУ |
|
dc.source.id |
SCOPUS17935571-2016-SID84992736468 |
|