ET-coessential and ET-coclosed submodules

Abstract EN

Let M be an R-module, where R be a commutative;ring with identity.

In this paper, we defined a new kind of submodules, namely; ET-coessential and ET-Coclosed submodules of M.

Let T be a submodule of M.

Let K H M, K is called ET-Coessential of H in M (K⊆ET.ce H), if .

A submodule H is called ET- coclosed in M of H has no proper coessential submodule in M, we denote by (K⊆ET.cc H) , that is, K⊆ET.ce H implies that K = H.

In our work, we introduce;some properties of ET-coessential and ET-coclosed submodules of M.