Zariski Topologies for Coprime and Second Submodules

Let $M$ be a non-zero module over an associative (not necessarily commutative) ring. In this paper, we investigate the so-called \emph{second} and \emph{coprime} submodules of $M.$ Moreover, we topologize the spectrum $$ of second submodules of $M$ and the spectrum $$ of coprime submodules of $M,$ study several properties of these spaces and investigate their interplay with the algebraic properties of $M.$

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