Article
| Title: | Maximal non-pseudovaluation subrings of an integral domain (English) |
| Author: | Kumar, Rahul |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 74 |
| Issue: | 2 |
| Year: | 2024 |
| Pages: | 389-395 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | The notion of maximal non-pseudovaluation subring of an integral domain is introduced and studied. Let $R\subset S$ be an extension of domains. Then $R$ is called a maximal non-pseudovaluation subring of $S$ if $R$ is not a pseudovaluation subring of $S$, and for any ring $T$ such that $R \subset T\subset S$, $T$ is a pseudovaluation subring of $S$. We show that if $S$ is not local, then there no such $T$ exists between $R$ and $S$. We also characterize maximal non-pseudovaluation subrings of a local integral domain. (English) |
| Keyword: | maximal non-pseudovaluation domain |
| Keyword: | pseudovaluation subring |
| MSC: | 13B02 |
| MSC: | 13B22 |
| MSC: | 13G05 |
| DOI: | 10.21136/CMJ.2024.0122-23 |
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| Date available: | 2024-07-10T14:50:16Z |
| Last updated: | 2024-07-15 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152447 |
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