A Module Whose Second Spectrum Has the Surjective or Injective Natural Map

Habibollah Ansari-Toroghy, Seyed sajad Pourmortazavi


‎Let $R$ be a commutative ring and $M$ be an $R$-module‎. ‎Let $Spec^{s}(M)$ be the set of all second submodules of $M$‎. In this article‎, ‎we topologize $Spec^{s}(M)$ with Zariski and classical Zariski topologies and study the classes of all modules whose second spectrum have the surjective or injective natural map‎. ‎Moreover‎, ‎we investigate the interplay between the algebraic properties of $M$ and the topological properties of $Spec^{s}(M)$‎.


Cotop module; second submodule; $X^{s}$-injective module; Zariski topology

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