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

Authors

  • Habibollah Ansari-Toroghy University of guilan
  • Seyed sajad Pourmortazavi University of guilan

Keywords:

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

Abstract

‎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 $Spec^{s}(M)$‎.

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Published

2017-02-03

Issue

Vol. 10 No. 2: (January 2017)

Section

Algebra

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How to Cite

A Module Whose Second Spectrum Has the Surjective or Injective Natural Map. (2017). European Journal of Pure and Applied Mathematics, 10(2), 211-230. https://www.ejpam.com/index.php/ejpam/article/view/2803