A basic associativity theorem for alternative algebras
A note on the number of generators of a nodal algebra
Alternative real division algebras of finite dimension.
Alternative rings in which every proper right ideal is maximal
Alternative Tripelsysteme.
Continuity of derivations on a complete normed alternative algebra
Der Wedderburnsche Hauptsatz für alternative Tripelsysteme und Paare.
Enveloping algebras of Malcev algebras
We first discuss the construction by Pérez-Izquierdo and Shestakov of universal nonassociative enveloping algebras of Malcev algebras. We then describe recent results on explicit structure constants for the universal enveloping algebras (both nonassociative and alternative) of the 4-dimensional solvable Malcev algebra and the 5-dimensional nilpotent Malcev algebra. We include a proof (due to Shestakov) that the universal alternative enveloping algebra of the real 7-dimensional simple Malcev algebra...
Exceptional prime alternative algebras.
Existence of Schütte semiautomorphisms
Finite-dimensional Left Moufang Algebras.
Formes quadratiques et algèbres quadratiques
Hom-Akivis algebras
Hom-Akivis algebras are introduced. The commutator-Hom-associator algebra of a non-Hom-associative algebra (i.e. a Hom-nonassociative algebra) is a Hom-Akivis algebra. It is shown that Hom-Akivis algebras can be obtained from Akivis algebras by twisting along algebra endomorphisms and that the class of Hom-Akivis algebras is closed under self-morphisms. It is pointed out that a Hom-Akivis algebra associated to a Hom-alternative algebra is a Hom-Malcev algebra.
Homotopes of Alternative Algebras.
Infinite independent systems of identities of alternative commutative algebra over a field of characteristic three
Let 𝔄₃ denote the variety of alternative commutative (Jordan) algebras defined by the identity x³ = 0, and let 𝔖₂ be the subvariety of the variety 𝔄₃ of solvable algebras of solviability index 2. We present an infinite independent system of identities in the variety 𝔄₃ ∩ 𝔖₂𝔖₂. Therefore we infer that 𝔄₃ ∩ 𝔖₂𝔖₂ contains a continuum of infinite based subvarieties and that there exist algebras with an unsolvable words problem in 𝔄₃ ∩ 𝔖₂𝔖₂. It is worth mentioning that these results were...
Invariants of Lie color algebras acting on graded algebras
We prove a series of "going-up" theorems contrasting the structure of semiprime algebras and their subalgebras of invariants under the actions of Lie color algebras.
Irreducible binary -bimodules over simple finite-dimensional algebras.
Jacobson's theorem for alternative rings
Lattice isomorphisms of alternative algebras
Linksquasialternative reelle Divisionsalgebren endlichen Ranges.