Essential Submodules with respect to an Arbitrary Submodule

Authors

  • Saeed Safaeeyan
  • Najmeh Saboori Shirazi

DOI:

https://doi.org/10.30495/jme.v7i0.213

Keywords:

Essential submodules, s-essential submodules, socle of a module

Abstract

The concept of essential submodules is a well known concept.In this paper we try to replace an arbitrary submodule of M,say T, instead of 0 in the definition of essential submodules. By this,essential submodules are precisely {0}-essential submodules. For a submoduleK of right R-module M, we have K ess M if and only if(K : m) is annr(m)-essential right ideal of R, for each m 2 M \ {0}.Among other things, this generalization of essential submodules gives anecessary and sufficient condition for MT being finitely co-generated.

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Published

2014-02-09

Issue

Vol. 7

Section

Vol. 7, No. 3, (2013)

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