Tr-Rationally Closed Submodules and RCLS-Modules

Abstract

: In this paper, we introduce two concepts. Firstly, the, concept of Tr-rationally closed,a sub module H is called Tr-rationally closed if W/H is Tr-torsion free. And second, the concept of Rcls-module, W is called Rcls-module if every Tr-rationally closed sub module in W is a direct summand. Several properties about these two concepts have been given. In addition, we discussed these notions with other related concepts.

P-Rational Submodules

“…Finally, it is important to remember that, as we noted earlier, there are relatively few references that have been concerned with studying rational submodules such as [15] and [18][19][20][21][22], which is what motivated us to carry out this study.…”