Wang's theorem for one-dimensional local rings

Abstract

In this article, we show that, Q:_A 𝔪^t ⊆ 𝔪^t for all integers t > 0, and for all parameter ideals Q ⊆ 𝔪^2t−1 in a one-dimensional Cohen-Macaulay local ring (A,𝔪) provided that A is not a regular local ring. The assertion obtained by Wang can be extended to one-dimensional (hence, arbitrary dimensional) local rings after some mild modifications. We refer to these quotient ideals I = Q:_A 𝔪^t, t-th quasi-socle ideals of Q. Examples are explored.