| Title:
|
On rings close to regular and $p$-injectivity (English) |
| Author:
|
Ming, Roger Yue Chi |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
47 |
| Issue:
|
2 |
| Year:
|
2006 |
| Pages:
|
203-212 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The following results are proved for a ring $A$: (1) If $A$ is a fully right idempotent ring having a classical left quotient ring $Q$ which is right quasi-duo, then $Q$ is a strongly regular ring; (2) $A$ has a classical left quotient ring $Q$ which is a finite direct sum of division rings iff $A$ is a left $\operatorname{TC}$-ring having a reduced maximal right ideal and satisfying the maximum condition on left annihilators; (3) Let $A$ have the following properties: (a) each maximal left ideal of $A$ is either a two-sided ideal of $A$ or an injective left $A$-module; (b) for every maximal left ideal $M$ of $A$ which is a two-sided ideal, $A/M_A$ is flat. Then, $A$ is either strongly regular or left self-injective regular with non-zero socle; (4) $A$ is strongly regular iff $A$ is a semi-prime left or right quasi-duo ring such that for every essential left ideal $L$ of $A$ which is a two-sided ideal, $A/L_A$ is flat; (5) $A$ prime ring containing a reduced minimal left ideal must be a division ring; (6) A commutative ring is quasi-Frobenius iff it is a $\operatorname{YJ}$-injective ring with maximum condition on annihilators. (English) |
| Keyword:
|
strongly regular |
| Keyword:
|
$p$-injective |
| Keyword:
|
$\operatorname{YJ}$-injective |
| Keyword:
|
biregular |
| Keyword:
|
von Neumann regular |
| MSC:
|
16D40 |
| MSC:
|
16D50 |
| MSC:
|
16E50 |
| MSC:
|
16N60 |
| idZBL:
|
Zbl 1106.16003 |
| idMR:
|
MR2241527 |
| . |
| Date available:
|
2009-05-05T16:56:47Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119587 |
| . |
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