On left annihilating content polynomials and power series

Let R be an associative unital ring, and let f∈R[x]. We say that f is a left annihilating content (AC) polynomial if f = af1 for some a∈R and f1∈R[x] with lR[x](f1)=0. The ring R is called a left EM-ring if each f∈R[x] is a left AC polynomial. In this paper, it is shown that R is a left EM-ring if and only if R is a left McCoy ring, and for each finitely generated right ideal I of R, there is an element a∈R and a finitely generated right ideal J of R with lR(J)=0 and I = aJ. If R is a left duo right Bezout ring, then R is a left EM-ring and has property (A). For a unique product monoid G, we show that if R is a reversible left EM-ring, then the monoid ring R[G] is also a left EM-ring. Additionally, for a reversible right Noetherian ring R, we prove that R, R[x],R[x,x−1], and R[[x]] are all simultaneously left EM-rings. Finally, we give an application of left EM-rings (resp. strongly left EM-rings) in studying the graph of zero-divisors of polynomial rings (resp. power series rings).