On the minimal submodules of a module

Authors

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

Keywords:

Second submodule, minimal submodule, Zariski topology, spectral space

Abstract

‎For any module $M$ over a commutative ring $R$‎, ‎$Spec^{s}_{R}(M)$ (resp‎. ‎$Min_{R}(M)$)‎ is the collection of all second (resp‎. ‎minimal) submodules of $M$‎. ‎In this article we investigate‎ ‎the interplay between the topological properties of $Min_{R}(M)$ and module theoretic properties of‎ ‎$M$‎. ‎Also‎, ‎for various types of modules $M$‎, ‎we obtain some conditions under which $Min_{R}(M)$‎ ‎is homeomorphic with the maximal ideal space of some ring‎.

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Published

2017-06-20

Issue

Vol. 72 No. 1 (2017)

Section

Articoli

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