Article
| Title: | Left EM rings (English) |
| Author: | Baeck, Jongwook |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 74 |
| Issue: | 3 |
| Year: | 2024 |
| Pages: | 839-867 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $R[x]$ be the polynomial ring over a ring $R$ with unity. A polynomial $f(x)\in R[x]$ is referred to as a left annihilating content polynomial (left ACP) if there exist an element $r \in R$ and a polynomial $g(x) \in R[x]$ such that $f(x)=rg(x)$ and $g(x)$ is not a right zero-divisor polynomial in $R[x]$. A ring $R$ is referred to as left EM if each polynomial $f(x) \in R[x]$ is a left ACP. We observe the structure of left EM rings with various properties, and study the relationships between the one-sided EM condition and other standard ring theoretic conditions. Moreover, several extensions of EM rings are investigated, including polynomial rings, matrix rings, and Ore localizations. (English) |
| Keyword: | EM ring |
| Keyword: | annihilating content polynomial |
| Keyword: | polynomial ring |
| Keyword: | uniserial ring |
| Keyword: | generalized morphic ring |
| Keyword: | zero-divisor |
| MSC: | 16E50 |
| MSC: | 16P40 |
| MSC: | 16U80 |
| MSC: | 16W99 |
| DOI: | 10.21136/CMJ.2024.0071-24 |
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| Date available: | 2024-10-03T12:38:14Z |
| Last updated: | 2024-10-04 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152584 |
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