Related papers: On graded $S$-comultiplication modules

Let R be a commutative ring with unity and M be an R- module In this paper we introduce semi n- absorbing and (k, n)-closed submodules of modules over commutative rings, and investigate their basic properties.

Let $R$ be a $G$-graded ring. In this article, we introduce two new concepts on graded rings, namely, weakly graded rings and invertible graded rings, and we discuss the relations between these concepts and several properties of graded…

For a proper submodule $N$ of a finitely generated module $M$ over a Noetherian ring, the product of prime ideals which occur in a regular prime extension filtration of $M$ over $N$ is defined as its generalized prime ideal factorization in…

In this paper, all rings are commutative with nonzero identity. Let $M$ be an $R$-module. A proper submodule $N$ of $M$ is called a classical prime submodule, if for each $m\in M$ and elements $a,b\in R$, $abm\in N$ implies that $am\in N$…

We prove that for any finite-dimensional differential graded algebra with separable semisimple part the category of perfect modules is equivalent to a full subcategory of the category of perfect complexes on a smooth projective scheme with…

Let $A$ be a commutative noetherian ring, let $\mathfrak a$ be an ideal of $A$ and let $n$ be a non-negative integer. In this paper, we study $\mathcal{S}_{n}(\mathfrak{a})$, a certain class of $A$-modules and we find some sufficient…

Let R be a commutative ring with unity, M a module over R and let S be a G-set for a finite group G. We define a set MS to be the set of elements expressed as the formal finite sum of the form similar to the elements of group ring RG. The…

Let $R=\bigoplus_{i\geq 0}R_i$ be a Noetherian commutative non-negatively graded ring such that $(R_0,\mathfrak{m}_0)$ is a Henselian local ring. Let $\mathfrak{m}$ be its unique graded maximal ideal $\mathfrak{m}_0+\bigoplus_{i>0}R_i$. Let…

In this paper, we dualize the concept of {\Sigma}-Rickart modules as {\Sigma}-dual Rickart modules. An R-module M is said to be {\Sigma}-dual Rickart if the direct sum of arbitrary copies of M is dual Rickart. We prove that each…

In this paper we explore the possibility of endowing simple infinite-dimensional ${\mathfrak{sl}_2(\mathbb{C})}$-modules by the structure of the graded module. The gradings on finite-dimensional simple module over simple Lie algebras has…

Let $G$ be the simple algebraic group $SL_2$ defined over an algebraically closed field $K$ of characteristic $p>0$. In this paper, we find the second cohomology of all irreducible representations of $G$

Let $R$ be a commutative ring with non-zero identity and $M$ be a unitary $R$-module. Let $\mathcal{S}(M)$ be the set of all submodules of $M$, and $\phi:\mathcal{S}(M)\to \mathcal{S}(M)\cup \{\emptyset\}$ be a function. We say that a…

We provide a framework connecting several well known theories related to the linearity of graded modules over graded algebras. In the first part, we pay a particular attention to the tensor products of graded bimodules over graded algebras.…

Let $ m , n \in \mathbb{N}$, $D$ be a division ring, and $M_{m \times n}(D)$ denote the bimodule of all $m \times n$ matrices with entries from $D$. First, we characterize one-sided submodules of $M_{m \times n}(D)$ in terms of left row…

We define a cotriple (co)homology of crossed modules with coefficients in a $\pi_1$-module. We prove its general properties, including the connection with the existing cotriple theories on crossed modules. We establish the relationship with…

In this paper, we introduce and investigate some properties of $\phi$-$\delta$-$S$-primary submodules, which is a generalization of the $\phi$-$\delta$-primary submodules and prime submodules in general. We extend a number of main results…

In this work, we extend the definition of the graded prime ideals from those in commutative graded rings to the ideals over graded Lie algebras. We prove some facts about graded prime Lie ideals in arbitrary Lie algebras that are similar to…

The main result of this article is a fantastic generalization of a classical result in graded ring theory. In fact, our result states that if $S$ is a multiplicative set of homogeneous elements of an $M$-graded commutative ring…

Let S be a finitely generated standard multi-graded algebra over a Noetherian local ring A. This paper first expresses mixed multiplicities of S in term of Hilbert-Samuel multiplicity that explained the mixed multiplicities S as the…

Any Z_2-graded C*-dynamical system with a self-adjoint graded-KMS functional on it can be represented (canonically) as a Z_2-graded algebra of bounded operators on a Z_2-graded Hilbert space, so that the grading of the latter is compatible…