Wang's theorem for one-dimensional local rings

Abstract

In this article, we show that, $Q:_A\frak{m}^t\subseteq\frak{m}^t$ for all integers $t$ > 0, and for all parameter ideals $Q\subseteq\frak{m}^{2t-1}$ in a one-dimensional Cohen-Macaulay local ring $(A,\frak{m})$ 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 $I = Q:_A\frak{m}^t$, $t$-th quasi-socle ideals of $Q$. Examples are explored.