| Abstrak/Abstract |
Let R be a commutative ring with identity and f (x) is a zero divisor polynomial in R[x]. If f (x) = c f g(x) with c f ∈ R
and g(x) ∈ R[x] is not a zero divisor, then c f 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 annihilating
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 ) = c fC(g) is the sufficient and necessary condition for c f 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. |
