δ-Small submodule and Lifting property

Abstract

In this paper, T is a commutative ring with identity. We were interested in providing A new conclusion about -small submodule by clarifying the connection between the lifting module and -small submodule. Moreover, by employing the concept -projective cover we illustrate how to put any submodule of the module as -small. In addition, we state the definition of -lifting module and associate it with additional concepts such as finitely generated and the property of cyclic module known as principally -lifting to get -small. Lastly, we explained the relationship between p- - hollow and -small in a certain conditions.