A generalisation of Amitsur's A-polynomials
We find examples of polynomials whose eigenring is a central simple algebra over the field .
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Cartan subalgebras, weight spaces, and criterion of solvability of finite dimensional Leibniz algebras.
Sergio A. Albeverio, Ayupov, Shavkat, A. 2, Bakhrom A. Omirov (2006)
Revista Matemática Complutense
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.
J. Dixmier (1984)
Journal für die reine und angewandte Mathematik
Classification of 4-dimensional nilpotent complex Leibniz algebras.
Sergio Albeverio, Bakhrom A. Omirov, Isamiddin S. Rakhimov (2006)
Extracta Mathematicae
Combinaisons non-associatives
Monique Bertrand (1962/1963)
Séminaire Dubreil. Algèbre et théorie des nombres
Déformation des algèbres de Bernstein normales.
Moussa Ouattara (1987)
Extracta Mathematicae
Derivationen und Automorphismen von Algebren, in denen die Gleichung x2 = 0 nur trivial lösbar ist.
Claus Sprengelmeier (1979)
Manuscripta mathematica
Direct product decomposition of zero-product-associative rings without nilpotent elements
Alexander Abian (1978)
Colloquium Mathematicae
Division algebras that generalize Dickson semifields
Daniel Thompson (2020)
Communications in Mathematics
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.
David R. Finston (1987)
Manuscripta mathematica
Eight-dimensional real absolute-valued algebras with left unit whose automorphism group is trivial.
Rochdi, A. (2003)
International Journal of Mathematics and Mathematical Sciences
Loops embedded in generalized Cayley algebras of dimension , .
Cawagas, Raoul E. (2001)
International Journal of Mathematics and Mathematical Sciences
Moufang H*-algebras.
José Antonio Cuenca Mira (2002)
Extracta Mathematicae
Nondegenerate invariant bilinear forms on nonassociative algebras.
Bordemann, M. (1997)
Acta Mathematica Universitatis Comenianae. New Series
On Algebras all of Whose Subalgebras are Simple; Some Solutions of Plonka's Problem
Sin-Min Lee (1985)
Publications de l'Institut Mathématique
On Herstein's theorems relating modularity in A and A(+).
José A. Anquela (1992)
Extracta Mathematicae
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
Vasiliy A. Chupordia, Leonid A. Kurdachenko, Igor Ya. Subbotin (2022)
Commentationes Mathematicae Universitatis Carolinae
We begin to study the structure of Leibniz algebras having maximal cyclic subalgebras.
On some properties of the upper central series in Leibniz algebras
Leonid A. Kurdachenko, Javier Otal, Igor Ya. Subbotin (2019)
Commentationes Mathematicae Universitatis Carolinae
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
Tomáš Kepka (1993)
Commentationes Mathematicae Universitatis Carolinae
A ring or an idempotent semiring is associative provided that additive endomorphisms are multiplicative.
(T)-algèbres non associatives
Marie-Christine Germa (1966/1967)
Séminaire Dubreil. Algèbre et théorie des nombres
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