6 citations · 6 across the 7 of their papers we have counts for
7 papers
A vanishing criterion for Lie elements in a free Novikov algebra
F. A. Mashurov, B. K. Sartayev
Every Novikov algebra is Lie-admissible: the commutator turns it into a Lie algebra. We give a finite criterion for a multilinear element of the free Novikov algebra to belong to t…
A polynomial criterion for Jordan elements in a free associative algebra
F. Mashurov, B. Sartayev
Let be the Jordan subalgebra of the free associative algebra $\Q\langle X\rangle$ generated by and under . We give a polynomial criterion for…
Free Novikov-Zinbiel algebra
A. Dauletiyarova, F. Mashurov, B. Sartayev
Let be a commutative-associative algebra with an invertible derivation , and put . We study the operations \begin{equation*} x\succ y=R(x)y,\qquad x\prec y=xD(y),…
On the free metabelian transposed Poisson and F-manifold algebras
K. Abdukhalikov, B. K. Sartayev
In this paper, we consider free transposed Poisson algebra and free F-manifold algebra with an additional metabelian identity. We construct a linear basis for both free metabelian…
On the free metabelian Novikov and metabelian Lie-admissible algebras
A. Dauletiyarova, K. Abdukhalikov, B. K. Sartayev
In this paper, we consider Lie-admissible algebras, which are free Novikov and free Lie-admissible algebras with an additional metabelian identity. We construct a linear basis for…
Binary perm algebras and alternative algebras
A. Kunanbayev, B. K. Sartayev
In this paper, we describe the defining identities of a variety of binary perm algebras, which is a subvariety of the variety of alternative algebras. In addition, we construct a b…
Novikov dialgebras and perm algebras
F. Mashurov, B. K. Sartayev
In this paper, we consider Perm algebra with the derivation . The algebra itself is equipped with the new operation . We construct a linear basis of the free…