22 citations · 48 across the 14 of their papers we have counts for
5 papers · 1 filter
Special identities of nonsymmetric bicommutative operations in associative algebra with an operator
Bauyrzhan Sartayev, Abdibek Ydyrys
Let be an associative non-unital algebra with a linear operator satisfying \[aS(S(b)c)=S(aS(b))c,\] and define and . We determine the speci…
A unified approach to the definition of anti-algebras
Ivan Kaygorodov, Abror Khudoyberdiyev, Bauyrzhan Sartayev
We introduce the arseille anti-construction for varieties of algebras defined by multilinear identities of degree , obtained by changing the sign of…
The Weight Criterion, Dong Property, and Manin Products of Operads
P. Kolesnikov, B. Sartayev
We establish that, for a binary operad Var, the Hadamard product of Var and the operad Nov of Novikov algebras is a binary operad (i.e., coincides with their Manin white product No…
Initial pre-algebras as a generalization of dendriform algebras
P. S. Kolesnikov, B. K. Sartayev
We continue the study of \emph{initial dialgebras} defined in~\cite{DMS2026}. For a binary operad $\Var$ we define the class of initial pre-$\Var$-algebras and the corresponding op…
Malcev classification for the variety of left-symmetric algebras
A. Ryskeldin, B. Sartayev
In this paper, we study three classes of subvarieties inside the variety of left-symmetric algebras. We show that these subvarieties are naturally related to some well-known variet…