2-Visible Submodules and Fully 2-Visible Modules

Abstract

Let X be a T -module, T is a commutative ring with identity and K be a proper submodule of X. In this paper we introduce the concepts of 2-visible submodules and fully 2-visible modules as a generalizations of visible submodules and fully visible modules resp., where K is said to be 2-visible whenever K=I2 K for every nonzero ideal I of T and AT -module X is called fully 2-visible if for any proper submodule of it is 2-visible.Study some of the properties of these concepts also discuss the relationship 2-visible submodules and fully 2-visible modules with 2-pure submoules and other related submodules and modules resp. are given

Keywords

• visible submodules; 2-visible submodules; 2-pure submoules; strongly cancellation module; fully visible modules; fully 2-visible modules