Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal, Vol. 74, No. 3, pp. 839-867, 2024

Left EM rings

Jongwook Baeck

Received February 18, 2024. Published online July 15, 2024.

Abstract: 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.

Keywords: EM ring; annihilating content polynomial; polynomial ring; uniserial ring; generalized morphic ring; zero-divisor

Classification MSC: 16U80, 16W99, 16E50, 16P40

DOI: 10.21136/CMJ.2024.0071-24

PDF available at: Springer Institute of Mathematics CAS Digital Mathematics Library

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Affiliations: Jongwook Baeck, School of Basic Sciences, Hanbat National University, Yuseong Deokmyeong Campus, Dongseo-daero, Yuseong-gu, Daejeon 34158, South Korea, e-mail: jubaik@hanbat.ac.kr

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