English

Classical 2-absorbing submodules of modules over commutative rings

Commutative Algebra 2015-05-26 v1

Abstract

In this article, all rings are commutative with nonzero identity. Let MM be an RR-module. A proper submodule NN of MM is called a classical prime submodule, if for each mMm\in M and elements a,bRa,b\in R, abmNabm\in N implies that amNam\in N or bmNbm\in N. We introduce the concept of "classical 2-absorbing submodules" as a generalization of "classical prime submodules." We say that a proper submodule NN of MM is a classical 2-absorbing submodule if whenever a,b,cRa,b,c\in R and mMm\in M with abcmNabcm\in N, then abmNabm\in N or acmNacm\in N or bcmNbcm\in N.

Keywords

Cite

@article{arxiv.1505.06564,
  title  = {Classical 2-absorbing submodules of modules over commutative rings},
  author = {Hojjat Mostafanasab and Unsal Tekir and Kursat Hakan Oral},
  journal= {arXiv preprint arXiv:1505.06564},
  year   = {2015}
}

Comments

13 pages

R2 v1 2026-06-22T09:40:41.787Z