CENTER OF NOETHERIAN RINGS

Abstract

For a right Noetherian ring A with the center R = Z(A), and a finitely generated right A-module M, we show: (1) P ∈ Ass(M) implies that P ∩R ∈ Supp(M). (2) P ∈ Min.Supp(M) implies that there exists Q ∈ Ass(M) such that Q∩R = P. This result has several applications in determining the nilradical of the center of a Noetherian ring. We also give a conceptually simple proof of the fact that the center of an Artinian ring is semiprimary. Some other related results are obtained for irreducible rings.