3 Results Found

Let R be an associative ring with unity, X be a finite group, H be a subgroup of X, and $\mathfrak{G}$ be a set of left coset representatives for the left action of H on X. In this article, we introduce two different ways to put R into a non-trivial $\mathfrak{G}$-weak graded...

In this article, we generalize the concept of group-graded modules by introducing the concept of $\mathfrak{G}$-weak graded R-modules, which are R-modules graded by a set $\mathfrak{G}$ of left coset representatives, where R is a $\mathfrak{G}$-weak graded ring. Moreover, we prove some pr...

In this work, we use the concept of $\mathfrak{G}$-weak graded rings and $\mathfrak{G}$-weak graded modules, which are based on grading by a set $\mathfrak{G}$ of left coset representatives for the left action of a subgroup $\mathfrak{H}$ of a finite $\mathfrak{X}$ on $\mathfrak{X}$, to define the conjugation action of the set...