A generalisation of Amitsur's A-polynomials
We find examples of polynomials whose eigenring is a central simple algebra over the field .
Cartan subalgebras, weight spaces, and criterion of solvability of finite dimensional Leibniz algebras.
In this work the properties of Cartan subalgebras and weight spaces of finite dimensional Lie algebras are extended to the case of Leibniz algebras. Namely, the relation between Cartan subalgebras and regular elements are described, also an analogue of Cartan s criterion of solvability is proved.
Certaines algèbres non associatives simples définies par la transvection des formes binaires.
Classification of 4-dimensional nilpotent complex Leibniz algebras.
Combinaisons non-associatives
Déformation des algèbres de Bernstein normales.
Derivationen und Automorphismen von Algebren, in denen die Gleichung x2 = 0 nur trivial lösbar ist.
Direct product decomposition of zero-product-associative rings without nilpotent elements
Division algebras that generalize Dickson semifields
We generalize Knuth’s construction of Case I semifields quadratic over a weak nucleus, also known as generalized Dickson semifields, by doubling of central simple algebras. We thus obtain division algebras of dimension by doubling central division algebras of degree . Results on isomorphisms and automorphisms of these algebras are obtained in certain cases.
Edomorphisms and Null subalgeras of finite dimensional algebras.
Eight-dimensional real absolute-valued algebras with left unit whose automorphism group is trivial.
Loops embedded in generalized Cayley algebras of dimension , .
Moufang H*-algebras.
Nondegenerate invariant bilinear forms on nonassociative algebras.
On Algebras all of Whose Subalgebras are Simple; Some Solutions of Plonka's Problem
On Herstein's theorems relating modularity in A and A(+).
In this paper we will examine the relationship between modularity in the lattices of subalgebras of A and A(+), for A an associative algebra over an algebraically closed field. To this aim we will construct an ideal which measures the modularity of an algebra (not necessarily associative) in paragraph 1, examine modular associative algebras in paragraph 2, and prove in paragraph 3 that the ideal constructed in paragraph 1 coincides for A and A(+). We will also examine some properties of the ideal...
On Leibniz algebras with maximal cyclic subalgebras
We begin to study the structure of Leibniz algebras having maximal cyclic subalgebras.
On some properties of the upper central series in Leibniz algebras
This article discusses the Leibniz algebras whose upper hypercenter has finite codimension. It is proved that such an algebra includes a finite dimensional ideal such that the factor-algebra is hypercentral. This result is an extension to the Leibniz algebra of the corresponding result obtained earlier for Lie algebras. It is also analogous to the corresponding results obtained for groups and modules.
Semirings whose additive endomorphisms are multiplicative
A ring or an idempotent semiring is associative provided that additive endomorphisms are multiplicative.
(T)-algèbres non associatives