12 citations · 25 across the 17 of their papers we have counts for
22 papers
Alternative -algebras and ${\mit Γ}$-algebras
Alexandre Grishkov, Ivan Shestakov
Recently V.H.López Solís and I.Shestakov solved an old problem by N.Jacobson on describing of unital alternative algebras containing the matrix algebra as a unita…
Skew-symmetric identities of finitely generated alternative algebras
Ivan P. Shestakov
We prove that for every natural number n there exists a natural number N(n) such that every multilinear skew-symmetric polynomial on N(n) or more variables which vanishes in the fr…
New elements in the center of free alternative algebra
Ivan Shestakov, Sergey Sverchkov
A new series of central elements is found in the free alternative algebra. More exactly, let and be the free alternative algebra and the free spec…
LD-stability for Goldie rings
Vyacheslav Futorny, João Schwarz, Ivan Shestakov
The lower transcendence degree, introduced by J. J Zhang, is an important non-commutative invariant in ring theory and non-commutative geometry strongly connected to the classical…
Multi-component generalizations of mKdV equation and non-associative algebraic structures
Ivan P. Shestakov, Vladimir V. Sokolov
Relations between triple Jordan systems and integrable multi-component models of the modified Korteveg--de Vries type are established. The most general model is related to a pair c…
Loop of formal diffeomorphisms and F{à}a di Bruno coloop bialgebra
Alessandra Frabetti, Ivan Shestakov
We consider a generalization of (pro)algebraic loops defined on general categories of algebras and the dual notion of a coloop bialgebra suitable to represent them as functors. Our…