2021/02/24 by Celikel, Ece Yetkin
#Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2102.12148
Let R be a commutative ring with non-zero identity and M be a unitary R-module. The goal of this paper is to extend the concept of 1-absorbing primary ideals to 1-absorbing primary submodules. A proper submodule N of M is said to be a 1-absorbing primary submodule if whenever non-unit elements a,b∈ R and m∈ M with abm∈ N, then either ab∈(N:RM) or m∈ M-rad(N). Various properties and chacterizations of this class of submodules are considered. Moreover, 1-absorbing primary avoidance theorem is proved.