| Title:
|
A generalization of reflexive rings (English) |
| Author:
|
Çalcı, Mete Burak |
| Author:
|
Chen, Huanyin |
| Author:
|
Halıcıoğlu, Sait |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
149 |
| Issue:
|
2 |
| Year:
|
2024 |
| Pages:
|
225-235 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We introduce a class of rings which is a generalization of reflexive rings and $J$-reversible rings. Let $R$ be a ring with identity and $J(R)$ denote the Jacobson radical of $R$. A ring $R$ is called $J$-reflexive if for any $a, b \in R$, $aRb = 0$ implies $bRa \subseteq J(R)$. We give some characterizations of a $J$-reflexive ring. We prove that some results of reflexive rings can be extended to $J$-reflexive rings for this general setting. We conclude some relations between $J$-reflexive rings and some related rings. We investigate some extensions of a ring which satisfies the $J$-reflexive property and we show that the $J$-reflexive property is Morita invariant. (English) |
| Keyword:
|
reflexive ring |
| Keyword:
|
reversible ring |
| Keyword:
|
$J$-reflexive ring |
| Keyword:
|
$J$-reversible ring |
| Keyword:
|
ring extension |
| MSC:
|
13C99 |
| MSC:
|
16D80 |
| MSC:
|
16U80 |
| DOI:
|
10.21136/MB.2023.0034-22 |
| . |
| Date available:
|
2024-07-10T15:04:26Z |
| Last updated:
|
2024-07-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152469 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| . |
