# Zariski Topologies for Coprime and Second Submodules - Mathematics > Rings and Algebras

Abstract: Let $M$ be a non-zero module over an associative not necessarilycommutative ring. In this paper, we investigate the so-called \emph{second}and \emph{coprime} submodules of $M.$ Moreover, we topologize the spectrum $%\mathrm{Spec}^{\mathrm{s}}M$ of second submodules of $M$ and the spectrum $%\mathrm{Spec}^{\mathrm{c}}M$ of coprime submodules of $M,$ study severalproperties of these spaces and investigate their interplay with the algebraicproperties of $M.$