Open AccessOn S-2-absorbing primary submodules
Author(s) -
A Osama Naji
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2105477n
Subject(s) - mathematics , generalization , primary (astronomy) , element (criminal law) , ring (chemistry) , pure mathematics , arithmetic , discrete mathematics , combinatorics , mathematical analysis , physics , law , chemistry , organic chemistry , astronomy , political science
This article introduces the concept of S-2-absorbing primary submodule as a generalization of 2-absorbing primary submodule. Let S be a multiplicatively closed subset of a ring R and M an R-module. A proper submodule N of M is said to be an S-2-absorbing primary submodule of M if (N :R M) ? S = ? and there exists a fixed element s ? S such that whenever abm ? N for some a,b ? R and m ? M, then either sam ? N or sbm ? N or sab ? ?(N :R M). We give several examples, properties and characterizations related to the concept. Moreover, we investigate the conditions that force a submodule to be S-2-absorbing primary.