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Classical 2-Absorbing Submodules of Modules over Commutative Rings

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2015

Key Words:

Author NameUniversity of Author
Abstract (2. Language): 
In this article, all rings are commutative with nonzero identity. Let M be an R-module. A proper submodule N of M is called a classical prime submodule, if for each m " M and elements a, b " R, abm " N implies that am " N or bm " N. We introduce the concept of "classical 2-absorbing submodules" as a generalization of "classical prime submodules". We say that a proper submodule N of M is a classical 2-absorbing submodule if whenever a, b, c " R and m " M with abcm " N, then abm " N or acm " N or bcm " N.
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