Cosupport of artinian modules

Abstract

Let $(R,\mathfrak{m})$ be a commutative local noetherian ring. For an artinian $R$-module $M$, we show the equality $${\mathrm{cosupp}}_{R}M={\mathrm{Cosupp}}_{R}M$$ using the semi-discrete linearly compactness of $R$-module ${\mathrm{Hom}}_R(R_{\mathfrak{p}},M)$ where $\mathfrak{p}$ is a prime ideal of $R$.

arXiv comment7 pages,comments welcome