Recall that a ring $R\ $is said to be quasi regular if its total quotient $q(R)\ \textit{von Neumann regular}. It is well known and only it reduced satisfying the property: for each $a\in R,$ $ann_{R}(ann_{R}(a))=ann_{R}(b)$ some $b\in R$. Here, in this study, we extend notion of rings which satisfy aforementioned property modules. We give many characterizations properties these two classes Mor...

We develop the theory of coregular sequences and codepth for modules that need not be finitely generated or artinian over a Noetherian ring. use this to give new version theorem Hellus characterizing set-theoretic complete intersections in terms local cohomology modules. also define quasi-cyclic as increasing unions cyclic modules, show at least two are quasi-cyclic. then focus our attention on...