Results 21 to 30 of about 51 (43)
Values of the length function for nonassociative algebras [PDF]
arXiv, 2022 We study realizable values of the length function for unital possibly nonassociative algebras of a given dimension. To do this we apply the method of characteristic sequences and establish sufficient conditions of realisability for a given value of length.
arxiv
Homogeneous Multiplicative Polynomial Laws are Determinants [PDF]
arXiv, 2004 Let R be a ring and let B be a commutative ring. Let p be a homogeneous multiplicative polynomial law of degree n from R to B. We show that p is essentially a determinant, in the sense that p is obtained from a determinant by left and right composition with ring homomorphisms.
arxiv
Algebras of slowly growing length [PDF]
arXiv, 2022 We investigate the class of finite dimensional not necessary associative algebras that have slowly growing length, that is, for any algebra in this class its length is less than or equal to its dimension. We show that this class is considerably big, in particular, finite dimensional Lie algebras as well as many other important classical finite ...
arxiv
The structure of medial quandles [PDF]
arXiv, 2014 Medial quandles are represented using a heterogeneous affine structure. As a consequence, we obtain numerous structural properties, including enumeration of isomorphism classes of medial quandles up to 13 elements.
arxiv
Multiplicative generalized Jordan $n$-derivations of unital rings with idempotents [PDF]
arXiv, 2022 Let $\mathfrak{A}$ be a unital ring with a nontrivial idempotent. In this paper, it is shown that under certain conditions every multiplicative generalized Jordan $n$-derivation $\Delta:\mathfrak{A}\rightarrow\mathfrak{A}$ is additive. More precisely, it is proved that $\Delta$ is of the form $\Delta(t)=\mu t+\delta(t),$ where $\mu\in\mathcal{Z ...
arxiv
Subdirectly irreducible medial quandles [PDF]
arXiv, 2015 We describe all subdirectly irreducible medial quandles. We show that they fall within one of four disjoint classes. In particular, in the finite case they are either connected (and therefore Alexander quandles) or reductive. Moreover, we provide a representation of all non-connected subdirectly irreducible medial quandles.
arxiv
Hom-post-Lie modules, O-operators and some functors on Hom-algebras [PDF]
arXiv, 2016 The aim of this paper is to study modules over Hom-post-Lie algebras and give some contructions and various twisting i.e. we show that modules over post-Hom-Lie algebras are close by twisting either Hom-post-Lie algebras or module structure maps. Given a type of Hom-algebra A, an A-bimodule M and an O-operator T : A ---> M, we give constructions ...
arxiv
Lie Higher Derivations on Generalized Matrix Algebras [PDF]
arXiv, 2017 In this paper, at first the construction of Lie higher derivations and higher derivations on a generalized matrix algebra were characterized; then the conditions under which a Lie higher derivation on generalized matrix algebras is proper are provided. Finally, the applications of the findings are discussed.
arxiv
Multiplicative Lie derivation of triangular 3-matrix rings [PDF]
arXiv, 2020 A map $\phi$ on an associative ring is called a multiplicative Lie derivation if $\phi([x,y])=[\phi(x),y]+[x,\phi(y)]$ holds for any elements $x,y$, where $[x,y]=xy-yx$ is the Lie product. In the paper, we discuss the multiplicative Lie derivations on the triangular 3-matrix rings $\mathcal T={\mathcal T}_3(\mathcal R_i; \mathcal M_{ij})$.
arxiv
Lie Biderivations on Triangular Algebras [PDF]
arXiv, 2020 Let $\mathcal{T}$ be a triangular algebra over a commutative ring $\mathcal{R}$ and $\varphi: \mathcal{T} \times \mathcal{T}\longrightarrow \mathcal{T}$ be an arbitrary Lie biderivation of $\mathcal{T}$. We will address the question of describing the form of $\varphi$ in the current work.
arxiv