-гомоморфизмы колец
Ternärringe ohne Planaritätsbedingung
Ternary algebras and calculus of cubic matrices
We study associative ternary algebras and describe a general approach which allows us to construct various classes of ternary algebras. Applying this approach to a central bimodule with a covariant derivative we construct a ternary algebra whose ternary multiplication is closely related to the curvature of the covariant derivative. We also apply our approach to a bimodule over two associative (binary) algebras in order to construct a ternary algebra which we use to produce a large class of Lie algebras....
Ternary Jordan homomorphisms in -ternary algebras.
The classical Yang-Baxter equation on alternative algebras: the alternative -bialgebra structure on Cayley-Dickson matrix algebras.
The Conway-Norton algebras for ?(6,3), ?(7,3), F'24, and their full automorphism groups.
The fundamental theorem and Maschke's theorem in the category of relative Hom-Hopf modules
We introduce the concept of relative Hom-Hopf modules and investigate their structure in a monoidal category . More particularly, the fundamental theorem for relative Hom-Hopf modules is proved under the assumption that the Hom-comodule algebra is cleft. Moreover, Maschke’s theorem for relative Hom-Hopf modules is established when there is a multiplicative total Hom-integral.
The ideal structure of simple ternary algebras
The Leibniz algebras whose subalgebras are ideals
In this paper we obtain the description of the Leibniz algebras whose subalgebras are ideals.
The Levitzki Radical in Varieties of Algebras.
The local integration of Leibniz algebras
This article gives a local answer to the coquecigrue problem for Leibniz algebras, that is, the problem of finding a generalization of the (Lie) group structure such that Leibniz algebras are the corresponding tangent algebra structure. Using links between Leibniz algebra cohomology and Lie rack cohomology, we generalize the integration of a Lie algebra into a Lie group by proving that every Leibniz algebra is isomorphic to the tangent Leibniz algebra of a local Lie rack. This article ends with...
The Magic Square and symmetric Compositions.
The new construction given by Barton and Sudbery of the Freudenthal-Tits magic square, which includes the exceptional classical simple Lie algebras, will be interpreted and extended by using a pair of symmetric composition algebras, instead of the standard unital composition algebras.
The Magic Square and Symmetric Compositions II.
The Magnus embedding for right-symmetric algebras.
The -Lie property of the Jacobian as a condition for complete integrability.
The nilpotency of near-rings
The nilpotency of torsion-free rings with given type set
The nilpotency properties of the Leibniz algebra .
The orthogonal automorphism groups for -orthograded quasimonocomposition algebras of dimension 9 satisfying the conditions , .
The structure and representation of n-ary algebras of DNA recombination
In this paper we investigate the structure and representation of n-ary algebras arising from DNA recombination, where n is a number of DNA segments participating in recombination. Our methods involve a generalization of the Jordan formalization of observables in quantum mechanics in n-ary splicing algebras. It is proved that every identity satisfied by n-ary DNA recombination, with no restriction on the degree, is a consequence of n-ary commutativity and a single n-ary identity of the degree 3n-2....