相关论文: Lie Derivations of a Matrix Ring over an Associati…

Let $K$ be an algebraically closed field of characteristic zero, $P_n=K[x_1, ..., x_n]$ the polynomial ring, and $W_n(K)$ the Lie algebra of all $K$-derivations on $P_n$. One of the most important subalgebras of $W_n(K)$ is the triangular…

In this paper, we study the ring of invariants under the action of SL(m,K)\times SL(n,K) and SL(m,K)\times SL(n,K)\times SL(2,K) on the 3-dimensional array of indeterminates of form m\times n\times 2, where K is an infinite field. And we…

Let $\mathscr{R}$ be a prime ring of Char$(\mathscr{R}) \neq 2$ and $m\neq 1$ be a positive integer. If $S$ is a nonzero skew derivation with an associated automorphism $\mathscr{T}$ of $\mathscr{R}$ such that $([S([a, b]), [a, b]])^{m} =…

Let $n$ be a positive integer and $R=(M_{ij})_{1\leq i,j\leq n}$ be a generalized matrix ring. For each $1\leq i,j\leq n$, let $I_i$ be an ideal of the ring $R_i:=M_{ii}$ and denote $I_{ij}=I_iM_{ij}+M_{ij}I_j$. We give sufficient…

In this paper, we first introduce the concept of symmetric biderivation radicals and characteristic subalgebras of Lie algebras, and study their properties. Based on these results, we precisely determine biderivations of some Lie algebras…

Let $R$ be a 2-torsion free $\sigma$-prime ring, $U$ a nonzero square closed $\sigma$-Lie ideal of $R$ and let $d$ be a derivation of $R$. In this paper it is shown that: 1) If $d$ is centralizing on $U$, then $d = 0$ or $U \subseteq Z(R)$.…

In this paper, the determinants of $n\times n$ matrices over commutative finite chain rings and over commutative finite principal ideal rings are studied. The number of $n\times n$ matrices over a commutative finite chain ring ${R}$ of a…

Motivated by the works of Wang [Y. Wang, \textit{Lie (Jordan) derivations of arbitrary triangular algebras,} Aequationes Mathematicae, \textbf{93} (2019), 1221-1229] and Moafian et al. [F. Moafian and H. R. Ebrahimi Vishki, \textit{Lie…

Regular algebraic $K$-theory for groups is a homology theory for discrete groups closely connected (but different from) group homology. It also gives a version of algebraic $K$-theory for rings by the simple functorial mapping assigning to…

Let $\mathcal{I}(R)$ be the set of all ideals of a ring $R$, $\delta$ be an expansion function of $\mathcal{I}(R)$. In this paper, the $\delta$-$J$-ideal of a commutative ring is defined, that is, if $a, b\in R$ and $ab\in I\in…

The aim of this work is to study some lattice diagram determinants $\Delta_L(X,Y)$. We recall that $M_L$ denotes the space of all partial derivatives of $\Delta_L$. In this paper, we want to study the space $M^k_{i,j}(X,Y)$ which is defined…

Derivations extend the concept of differentiation from functions to algebraic structures as linear operators satisfying the Leibniz rule. In Lie algebras, derivations form a Lie algebra via the commutator bracket of linear endomorphisms.…

Let {\Lnk} be the class of all $n$-dimensional real solvable Lie algebras having $k$-dimensional derived ideals. In 2020 the authors et al. gave a classification of all non 2-step nilpotent Lie algebras of {\Li}. We propose in this paper to…

Given a minimal set of generators $\bold{x}$ of an ideal $I$ of height d in a regular local ring ($R, m, k$) we prove several cases for which the map $K_d(\bold{x}; R) \otimes k \to \Tor_d^R (R/I, k)$ is the 0-map. As a consequence of the…

Let $k[X] = k[x_{i,j}: i = 1,..., m; j = 1,..., n]$ be the polynomial ring in $m n$ variables $x_{i,j}$ over a field $k$ of arbitrary characteristic. Denote by $I_2(X)$ the ideal generated by the $2 \times 2$ minors of the generic $m \times…

Without the faithful assumption, we prove that every Jordan derivation on a class of path algebras of quivers without oriented cycles is a derivation and that every Lie derivation on such kinds of algebras is of the standard form.

In this paper, we address the additivity of $n$-multiplicative isomorphisms and $n$-multiplicative derivations on Gamma rings. We proved that, if $\M$ is a $\Gamma$-ring satisfying the some conditions, then any $n$-multiplicative…

Let $ X $ be an $ m \times n $ matrix of distinct indeterminates over a field $ K $, where $ m \le n $. Set the polynomial ring $ K[X] := K[X_{ij} : 1 \le i \le m, 1 \le j \le n] $. Let $ 1 \le k < l \le n $ be such that $ l - k + 1 \ge m…

Let R be a 2 torsion free semiprime ring and d a nonzero derivation. Further let A = O(R) be the orthogonal completion of R and B = B(C) the Boolean ring of C where C be the extended centroid of R. We show that if a[[d(x),x]^n- [y,…

For a group $G$, N-series $\cal G$ of $G$ and commutative ring $R$ let $I^n_{R,\cal G}(G)$, $n\ge 0$, denote the filtration of the group algebra $R(G)$ induced by $\cal G$, and $I_R(G)$ its augmentation ideal. For subgroups $H$ of $G$, left…