It is well known that there is a close connection between coherent sheaves on a projective space P(V ) where V is a a vector space over a field k, and finitely generated graded modules over the symmetric algebra S(V ). The Bernstein-Gelfand-Gelfand (BGG) correspondence [5] from 1978 relates coherent sheaves on P(V ) with graded modules over the exterior algebra Λ(V ∗) = ⊕Λi(V ∗) where V ∗ is th...

Let $G$ be a group with identity $e$. $R$ $G$-graded commutative ring, $M$ graded $R$-module and $A\subseteq h(R)$ multiplicatively closed subset of $R$. In this paper, we introduce the concept $A$-2-absorbing submodules as generalization 2-absorbing $A$-prime $M.$ We investigate some properties class submodules.

In this article, we generalize the concept of group-graded modules by introducing G-weak graded R-modules, which are R-modules a set G left coset representatives, where R is ring. Moreover, prove some properties these modules. Finally, results related to fields and their vector spaces deduced. Many considerable examples provided with more emphasis on symmetric group S3 dihedral D6, gives symmet...

Let $G$ be a group with identity $e$. $R$ commutative $G$-graded ring non-zero identity, $S\subseteq h(R)$ multiplicatively closed subset of and $M$ graded $R$-module. In this article, we introduce study the concept $S$-1-absorbing prime submodules. A submodule $N$ $(N:_{R}M)\cap S=\emptyset$ is said to prime, if there exists an $s_{g}\in S$ such that whenever $a_{h}b_{h'}m_{k}\in N$, then eith...

In this paper, we consider the classification of irreducible Zand Z2-graded modules with finite dimensional homogeneous subspaces over the Virasoro-like algebra. We first prove that such a module is a uniformly bounded module or a generalized highest weight module. Then we determine all generalized highest weight irreducible modules. As a consequence, we also determine all the modules with nonz...

We deene two (n + 1) graded Lie brackets on spaces of multilinear mappings. The rst one is able to recognize n-graded as-sociative algebras and their modules and gives immediately the correct diierential for Hochschild cohomology. The second one recognizes n-graded Lie algebra structures and their modules and gives rise to the notion of Chevalley cohomology.