Related papers: Generalized derivations with central values on lie…

Let $L$ be a Lie algebra over a field of characteristic different from $2$. If $L$ is perfect and centerless, then every skew-symmetric biderivation $\delta:L\times L\to L$ is of the form $\delta(x,y)=\gamma([x,y])$ for all $x,y\in L$,…

Assume $R$ is a local Cohen-Macaulay ring. It is shown that $\Ass_R (H^l_I(R))$ is finite for any ideal $I$ and any integer $l$ provided $\Ass_R (H^2_{(x,y)}(R))$ is finite for any $x,y\in R$ and $\Ass_R (H^3_{(x_1,x_2,y)}(R))$ is finite…

Let $R$ be an associative ring with a nonzero ideal $I$ and a semiprime ideal $T$ such that $T\subsetneq I.$ Let $K$ be a nonempty subset of $R$ and $d:R\to R$ be a derivation of $R$, if $[d(x),x]\in T$ for all $x\in K,$ then $d$ is said to…

This paper is devoted to the study of non-semisimple Lie algebras of the form $\mathcal{L} = \mathcal{S} \ltimes \mathcal{N}$ whose derivations are all inner. By generalizing the methods of Sato and Angelopoulos, we introduce new families…

It is well-known that the central extensions of the loop group of a compact, simple and 1-connected Lie group are parametrised by their level $k \in Z$. This article concerns the question how much can be said for arbitrary $k \in R$ and we…

Let $\mathcal{R}$ be a $2$-torsion free commutative ring with unity, $X$ a locally finite pre-ordered set and $I(X,\mathcal{R})$ the incidence algebra of $X$ over $\mathcal{R}$. If $X$ consists of a finite number of connected components, we…

We prove that a Lie nilpotent one-sided ideal of an associative ring $R$ is contained in a Lie solvable two-sided ideal of $R$. An estimation of derived length of such Lie solvable ideal is obtained depending on the class of Lie nilpotency…

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…

Let $R^h$ denote the polynomial ring in variables $x_1,\,\ldots,\, x_h$ over a specified field $K$. We consider all of these rings simultaneously, and in each use lexicographic (lex) monomial order with $x_1 > \cdots > x_h$. Given a fixed…

The additive (generalized) $\xi$-Lie derivations on prime algebras are characterized. It is shown, under some suitable assumption, that an additive map $L$ is an additive (generalized) Lie derivation if and only if it is the sum of an…

Let $G$ be a group and let $R$ be a $G$-graded ring. We show that a nonzero central idempotent in $R$ has finite support group in two broad settings: when $G$ is abelian, and when $G$ is arbitrary but the grading satisfies a certain…

An associative ring $A$ gives rise to the Lie ring $A^{(-)}=(A,[a,b ]=ab-ba)$. The subject of isomorphisms of Lie rings $A^{(-)}$ and $[A,A]$ has attracted considerable attention in the literature. We prove that if the identity element of…

In this paper we characterize hemirings in which all $h$-ideals or all fuzzy $h$-ideals are idempotent. It is proved, among other results, that every $h$-ideal of a hemiring $R$ is idempotent if and only if the lattice of fuzzy $h$-ideals…

Let G be a complex semisimple Lie group and H a complex closed connected subgroup. Let g and h be their Lie algebras. We prove that the regular representation of G in $L^2(G/H)$ is tempered if and only if the orthogonal of h in g contains…

We develop a theory of universal central extensions of Hom-Lie algebras. Classical results of universal central extensions of Lie algebras cannot be completely extended to Hom-Lie algebras setting, because of the composition of two central…

Let $D$ be a division ring with infinite center, $n$ be a positive integer and $w(x_1,x_2,\cdots, x_m)=1$ be a generalized group identity over the general linear group $\GL_n(D)$. The aim of this paper is to prove that every subnormal…

Let $f$ be a newform of weight $2k$ and let $\chi$ be an unramified imaginary quadratic Hecke character of infinity type $(2t, 0)$, for some integer $0 < t \leq k-1$. We show that the central derivative of the Rankin-Selberg $L$-function…

We initiate a study on a range of new generalized derivations of finite-dimensional Lie algebras over an algebraically closed field of characteristic zero. This new generalization of derivations has an analogue in the theory of associative…

Let $R$ be a 2-torsion free semiprime ring and $U$ a nonzero square closed Lie ideal of $R$. In this paper it is shown that if $f$ is either an endomorphism or an antihomomorphism of $R$ such that $f(U)=U,$ then $f$ is strong commutativity…

We develop a theory of universal central extensions for Hom-Lie antialgebra. It is proved that a Hom-Lie antialgebra admits a universal central extension if and only if it is perfect. Moreover, we show that the kernel of the universal…