Abstract In this paper, we introduce and investigate two weak versions of graded-Noetherian modules. Let G be an abelian group with an identity element denoted by 0, R be a commutative G -graded ring ...

Abstract In this paper, we introduce and investigate two weak versions of graded-Noetherian modules. Let G G be an abelian group with an identity element denoted by 0 0, R R be a commutative G G ...

In this work we study flat modules over commutative noetherian rings under two kinds of restriction: that the modules are either submodules of free modules or that they have finite rank. The first ...

In this note we show that a Noetherian module has a dual module if and only if it satisfies $AB5^\ast$. A connection between completeness and $AB5^\ast$ is also ...

1 Department of Mathematics, Faculty of Science, Cairo University, Cairo, Egypt &Department of Mathematics, Faculty of Science, King Abdulaziz University, KSA. In this paper we introduce and ...