P-Dense Submodules

Authors

  • Hossein Khabazian
  • Saeid Safaeeyan

DOI:

https://doi.org/10.30495/jme.v0i0.42

Keywords:

P-donse submodule and right Kasch module

Abstract

Let M and P be right R¡modules. A submodule K of an R¡module M is called P-dense if for each m ∈ M; (K : m) is a P-faithful right ideal of R: PR is nonsingular if and only if, for each R-module M; every essential submodule of M is a P-dense submodule. For any R-module M; we obtain P-rational extention of M and equivalent condition in order that M is equal with its P¡rational extention is found. An R-module P is called right Kasch if every simple R-module can be embedded in P. Finally, we given some equivalent conditions for an R-module P to be right Kasch.

Author Biographies

Hossein Khabazian

Department of Mathematical sciences Isfahan University of Technology Isfahan,Iran

Saeid Safaeeyan

Department of Mathematical sciences Isfahan University of Technology Isfahan, Iran

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Published

2008-03-01

Issue

Vol 3 (2008-2009)

Section

Vol. 3, No. 1 (2008)

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