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Vietnam Journal of Mathematics

, Volume 44, Issue 3, pp 477–484 | Cite as

Pseudo-Valuation Modules

  • Reza Jahani-NezhadEmail author
  • Foroozan Khoshayand
Article

Abstract

The aim of this paper is to generalize the notion of pseudo-valuation to modules over arbitrary commutative rings. We generalize the notion of strongly prime ideal, as defined in Badawi et al. (Lecture Notes in Pure and Applied Mathematics 185:57–67, 1997, to the notion of strongly prime submodule. We define a module M to be a pseudo-valuation module if every prime submodule of M is strongly prime. It is shown that if M has a maximal submodule N, then M is pseudo-valuation if and only if N is strongly prime. Also, we characterize strongly prime submodules in pseudo-valuation modules. We investigate some properties of these modules, and study relations between some structures and these modules.

Keywords

Strongly prime ideal Pseudo-valuation ring Uniserial module 

Mathematics Subject Classification (2010)

13A18 13A15 13A10 13F30 13F05 

Notes

Acknowledgments

We would like to thank the referee for the valuable suggestions and comments.

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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2015

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceUniversity of KashanKashanIslamic Republic of Iran

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