| Title:
|
Characterization of irreducible polynomials over a special principal ideal ring (English) |
| Author:
|
Boudine, Brahim |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
148 |
| Issue:
|
4 |
| Year:
|
2023 |
| Pages:
|
501-506 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A commutative ring $R$ with unity is called a special principal ideal ring (SPIR) if it is a non integral principal ideal ring containing only one nonzero prime ideal, its length $e$ is the index of nilpotency of its maximal ideal. In this paper, we show a characterization of irreducible polynomials over a SPIR of length $2$. Then, we give a sufficient condition for a polynomial to be irreducible over a SPIR of any length $e$. (English) |
| Keyword:
|
polynomial |
| Keyword:
|
irreducibility |
| Keyword:
|
commutative principal ideal ring |
| MSC:
|
13B25 |
| MSC:
|
13F20 |
| idZBL:
|
Zbl 07790599 |
| idMR:
|
MR4673833 |
| DOI:
|
10.21136/MB.2022.0187-21 |
| . |
| Date available:
|
2023-11-23T12:35:58Z |
| Last updated:
|
2024-12-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151970 |
| . |
| 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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