Left EM rings

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) = 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) ∈ 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.