2-Nil submodules of modules over commutative rings

Abstract

In this paper, we extend the notion of 2-nil ideal introduced by Yetkin Celikel in [E. Yetkin Celikel, 2-nil ideals of commutative rings, Bulletin of the Belgian Mathematical Society Simon Stevin 28(3) (2021).] to 2-nil submodule which is a subclass of 2-Absorbing primary submodules. Let M be an R-module and N be a proper submodule of M. We say that N is a 2-nil submodule of M if whenever a,b R, m M and abm N, then ab Nil(M) or am N or bm N. We study the properties of this concept and establish several characterizations. We also investigate the 2-nil ideals of amalgamation. The obtained results yield new original families of examples of 2-nil ideals. © 2023 World Scientific Publishing Company.