| Title:
|
About G-rings (English) |
| Author:
|
Mahdou, Najib |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
58 |
| Issue:
|
1 |
| Year:
|
2017 |
| Pages:
|
13-18 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we are concerned with G-rings. We generalize the Kaplansky's theorem to rings with zero-divisors. Also, we assert that if $R \subseteq T$ is a ring extension such that $mT\subseteq R$ for some regular element $m$ of $T$, then $T$ is a G-ring if and only if so is $R$. Also, we examine the transfer of the G-ring property to trivial ring extensions. Finally, we conclude the paper with illustrative examples discussing the utility and limits of our results. (English) |
| Keyword:
|
G-ring |
| Keyword:
|
pullback |
| Keyword:
|
trivial extension |
| MSC:
|
13D02 |
| MSC:
|
13D05 |
| idZBL:
|
Zbl 06736740 |
| idMR:
|
MR3631677 |
| DOI:
|
10.14712/1213-7243.2015.196 |
| . |
| Date available:
|
2017-03-12T16:32:30Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146024 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| . |
