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Left EM rings

Jongwook Baeck — 2024

Czechoslovak Mathematical Journal

Let R [ x ] be the polynomial ring over a ring R with unity. A polynomial f ( x ) R [ x ] is referred to as a left annihilating content polynomial (left ACP) if there exist an element r R and a polynomial g ( x ) R [ x ] such that f ( x ) = r g ( 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 ) 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,...

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