On application of annihilating content of polynomial on EM ring properties on R[x] and R[[x]]

Let R be a commutative ring with identity and f (x) is a zero divisor polynomial in R[x]. If f (x) = cf g(x) with cf ∈ R and g(x) ∈ R[x] is not a zero divisor, then cf is called an annihilating content for f (x). A ring where every zero-divisor polynomial in R[x] has an annihilating content is called an EM ring. Moreover, if every zero divisor formal power series in R[[x]] has an anni-hilating content and R is an EM-ring, then R is called a strongly EM-ring. In this paper, we discussed the property of annihilating content, EM-ring, strongly EM-ring, and the relationship between EM-ring and some other rings such as Noetherian ring, Bézout ring and Armendariz ring. In this paper, we prove that C(f) = cf C(g) is the sufficient and necessary condition for cf to be an annihilating content for f (x). We also find the following results: if a ring R is strongly EM-ring, then R[x] also a strongly EM-ring; a polynomial ring R[x] is a strongly EM-ring if the ring R is a strongly EM-ring and a cartesian product of strongly EM-rings is a strongly EM-ring too. Beside that we find the condition that makes Bézout ring and Armendariz ring are strongly EM-ring.