Abstract
Let R be an associative unital ring, and let . We say that f is a left annihilating content (AC) polynomial if f = af1 for some
and
with
. The ring R is called a left EM-ring if each
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
and a finitely generated right ideal J of R with
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
is also a left EM-ring. Additionally, for a reversible right Noetherian ring R, we prove that R,
, and
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).