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