Related papers: Generalized Homogeneous Derivations on Graded Ring…
In this paper, we show that if the product $(D_1D_2, d_1d_2)$ of generalized derivations $(D_1, d_1)$ and $(D_2, d_2)$ on an algebra $A$ is a generalized derivation, then $d_1D_2$ and $d_2D_1$ map $A$ into $\hbox{rad}(A)$. Also, for…
We introduce graded gamma rings from a more general point of view via methods developed by Krasner and Halberstadt for graded rings. We propose three equivalent aspects of studying graded gamma rings, nonhomogeneous, semihomogeneous and…
Vector fields with components which are generalized zero-forms are constructed. Inner products with generalized forms, Lie derivatives and Lie brackets are computed. The results are shown to generalize previously reported results for…
We study Ore localisation of differential graded algebras. Further we define dg-prime rings, dg-semiprime rings, and study the dg-nil radical of dg-rings. Then, we define dg-essential submodules, dg-uniform dimension, and apply all this to…
We develop the theory of central ideals on commutative rings. We introduce and study the central seminormalization of a ring in another one. This seminormalization is related to the theory of regulous functions on real algebraic varieties.…
We extend the classical notion of standardly stratified $k$-algebra (stated for finite dimensional $k$-algebras) to the more general class of rings, possibly without $1,$ with enough idempotents. We show that many of the fundamental…
The main goal of this article is to introduce the concept of $EM-G-$graded rings. This concept is an extension of the notion of $EM-$rings. Let $G$ be a group and $R$ be a $G-$graded commutative ring. The $G-$gradation of $R$ can be…
For a set-valued map, we characterize, in terms of its (unconvexified or convexified) graphical derivatives near the point of interest, positively homogeneous maps that are generalized derivatives in the sense of [20]. This result…
Let $A$ be a regular ring containing a field $K$ of characteristic zero and let $R = A[X_1,\ldots, X_m]$. Consider $R$ as standard graded with $\deg A = 0$ and $\deg X_i = 1$ for all $i$. Let $G$ be a finite subgroup of $GL_m(A)$. Let $G$…
Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative ring with identity and $M$ a graded $R$-module. In this paper, we introduce the concept of graded $I_{e}$-prime submodule as a generalization of a graded prime…
We investigate some general machinery for describing semidualizing modules over generic constructions like ladder determinantal rings with coefficients in a normal domain. We also pose and investigate natural localization questions that…
We describe a general setting for the definition of semi-infinite cohomology of finite dimensional algebras, and provide its categorical interpretation. We apply this interpretation to compute semi-infinite cohomology of some modules over…
A wide class of skew derivations on degree-one generalized Weyl algebras $R(a,\varphi)$ over a ring $R$ is constructed. All these derivations are twisted by a degree-counting extensions of automorphisms of $R$. It is determined which of the…
We study the general properties of commutative differential graded algebras in the category of representations over a reductive algebraic group with an injective central cocharacter. Besides describing the derived category of differential…
We introduce a new class of graded rings extending the class of generalized Weyl algebras. These rings are orders in crossed products of the most general type, and we introduce their basic structure theory. We provide an extensive list of…
In this paper, we study the solving degrees for affine semi-regular sequences and their homogenized sequences. Some of our results are considered to give mathematically rigorous proofs of the correctness of methods for computing Gr\"{o}bner…
Let $R$ be a prime ring of characteristic different from $2$, $U$ be its Utumi quotient ring, $C$ be its extended centroid and $L$ be a non-central Lie ideal of $R$. Suppose $F$ and $G$ are two non-zero $b$-generalized skew derivations of…
We introduce a lattice structure as a generalization of meet-continuous lattices and quantales. We develop a point-free approach to these new lattices and apply these results to $R$-modules. In particular, we give the module counterpart of…
We describe all inequalities among generalized diagonals in positive semi-definite matrices. These turn out to be governed by a simple partial order on the symmetric group. This provides an analogue of results of Drake, Gerrish, and…
Let $R$ be a commutative $G$-graded ring with a nonzero unity. In this article, we introduce the concept of graded radically principal ideals. A graded ideal $I$ of $R$ is said to be graded radically principal if $Grad(I)=Grad(\langle…