Let R be a G-graded ring. In this article, we introduce two new concepts on graded rings, namely, weakly rings and invertible discuss the relations between these several properties of rings. Also, study concept crossed products some defined product give relationship Moreover, in generalization for essential submodules, semi-uniform modules which is uniform modules.

Let $R= \oplus_{ \alpha \in G} R_{\alpha}$ be a commutative ring with unity graded by an arbitrary grading monoid $G$. For each positive integer, the notions of graded-n-coherent module and are introduced. In this paper many results generalized from $n$-coherent rings to graded-$n$-coherent rings. last section, we provide necessary sufficient conditions for trivial extension graded-valuation ri...

academic writing ability is an important goal that learners of english as a second language (esl) or english as a foreign language (efl) try to attain. while esl students’ academic writings have been widely explored, owing to few studies investigating appraisal resources in efl students’ argumentative writing, the gap still exists about efl students’ academic writing. this study aimed to see ho...

Let G be a group (monoid) with identity e and R commutative Krasner hyperring. In this paper, we introduce the concepts of graded absorbing hyperideals hyperring such as, 2-absorbing hyperideals, n-absorbing subhypermodules. Some basic properties these structures characterizations homogeneous components are proved.

in this paper, the influence of the constituent volume fractions by changing the values of the power-law exponent with uniform pressure on the vibration frequencies of reinforced functionally graded cylindrical shells is studied. the fgm shell with ring is developed in accordance to the volume fraction law from two constituents namely stainless steel and nickel. these constituents are graded th...

‎let $g$ be a locally compact abelian group‎. ‎the concept of a generalized multiresolution structure (gms) in $l^2(g)$ is discussed which is a generalization of gms in $l^2(mathbb{r})$‎. ‎basically a gms in $l^2(g)$ consists of an increasing sequence of closed subspaces of $l^2(g)$ and a pseudoframe of translation type at each level‎. ‎also‎, ‎the construction of affine frames for $l^2(g)$ bas...