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- Title
Weakly Classical Prime Submodules.
- Authors
MOSTAFANASAB, HOJJAT; TEKIR, ÜNSAL; ORAL, KÜRŞAT HAKAN
- Abstract
In this paper, 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 \weakly classical prime submodules" and we will show that this class of submodules enjoys many properties of weakly 2-absorbing ideals of commutative rings. A proper submodule N of M is a weakly classical prime submodule if whenever a, b ∈ R and m ∈ M with 0 ≠ abm ∈ N, then am ∈ N or bm ∈ N.
- Subjects
MODULES (Algebra); RING theory; COMMUTATIVE rings; MATHEMATICAL analysis; SET theory
- Publication
Kyungpook Mathematical Journal, 2016, Vol 56, Issue 4, p1085
- ISSN
1225-6951
- Publication type
Article
- DOI
10.5666/KMJ.2016.56.4.1085