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 [Formula: see text] be an [Formula: see text]-module and [Formula: see text] be a proper submodule of [Formula: see text]. We say that [Formula: see text] is a 2-nil submodule of [Formula: see text] if whenever [Formula: see text], [Formula: see text] and [Formula: see text], then [Formula: see text] or [Formula: see text] or [Formula: see text] 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.