| Title:
|
On $p$-injectivity, YJ-injectivity and quasi-Frobeniusean rings (English) |
| Author:
|
Yue Chi Ming, Roger |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
43 |
| Issue:
|
1 |
| Year:
|
2002 |
| Pages:
|
33-42 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A new characteristic property of von Neumann regular rings is proposed in terms of annihilators of elements. An ELT fully idempotent ring is a regular ring whose simple left (or right) modules are either injective or projective. Artinian rings are characterized in terms of Noetherian rings. Strongly regular rings and rings whose two-sided ideals are generated by central idempotents are characterized in terms of special annihilators. Quasi-Frobeniusean rings are characterized in terms of $p$-injectivity. Also, a commutative YJ-injective ring with maximum condition on annihilators and finitely generated socle is quasi-Frobeniusean. (English) |
| Keyword:
|
von Neumann regular |
| Keyword:
|
$V$-ring |
| Keyword:
|
Artinian ring |
| Keyword:
|
$p$-injectivity |
| Keyword:
|
YJ-injectivity |
| Keyword:
|
quasi-Frobeniusean |
| MSC:
|
16D30 |
| MSC:
|
16D36 |
| MSC:
|
16D50 |
| MSC:
|
16E50 |
| MSC:
|
16L60 |
| MSC:
|
16N60 |
| MSC:
|
16P20 |
| idZBL:
|
Zbl 1068.16004 |
| idMR:
|
MR1903305 |
| . |
| Date available:
|
2009-01-08T19:19:16Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119298 |
| . |
| Reference:
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| . |
