Some Homological Conjectures Over Idealization Rings
Some Homological Conjectures Over Idealization Rings
Let $(R,\mathfrak{m},k)$ be a Noetherian local ring and let $M$ be a finitely generated $R$-module. The main focus of this paper is to give positive answers for some long-standing homological conjectures over the idealization ring $R\ltimes M$. First, if $N$ is a $R\ltimes k$-module, we show that the vanishing of …