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 ...

I am confused about \bar {\rational}. It is a field and so has only maximal ideals; it is thus Noetherian as a ring. Rather, we are interested in an infinitely ascending chain of \rational-submodules ...

Due to a planned power outage on Friday, 1/14, between 8am-1pm PST, some services may be impacted. A line drawing of the Internet Archive headquarters building façade. An illustration of a magnifying ...

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 ...

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 ...