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 ...

Algebraic structures form the backbone of many modern mathematical theories, with module theory standing as a central discipline within abstract algebra. Modules, generalising the concept of vector ...