Article
| Title: | Semiclean and quasi-clean elements in rings (English) |
| Author: | Ma, Guanglin |
| Author: | Leroy, André |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 75 |
| Issue: | 4 |
| Year: | 2025 |
| Pages: | 1431-1441 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We prove uniquely semiclean rings are reduced and hence Abelian. The semiclean elements of $R$, $R[x]$, and $M_n(R)$ are compared. In particular, we show that the indeterminate $x$ is never semiclean. The 2-primality of a ring $R$ is characterized via the semiclean elements of $R[x]$. We also consider the quasi-clean elements of a ring $R$ and compare them with the semiclean elements of $R$. (English) |
| Keyword: | periodic element |
| Keyword: | semiclean element |
| Keyword: | 2-primal |
| Keyword: | polynomial ring |
| MSC: | 16P10 |
| MSC: | 16U40 |
| MSC: | 16U99 |
| DOI: | 10.21136/CMJ.2025.0290-25 |
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| Date available: | 2025-12-20T08:01:22Z |
| Last updated: | 2025-12-22 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153251 |
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