2015/05/25 by Mostafanasab, Hojjat, Tekir, Unsal, Oral, Kursat Hakan
#13A15 #13C99 #13F05 #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1505.06730
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." 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.