On S-2-absorbing primary submodules

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.