6 citations · 6 across the 5 of their papers we have counts for
5 papers
Radicals of Lie-solvable Novikov algebras
A. S. Panasenko
We prove that in a Lie-solvable Novikov algebra, the Baer radical coincides with the set of all right-nilpotent elements, and the Andrunakievich radical coincides with the largest…
Central orders in simple right-alternative superalgebras and right-symmetric algebras
A. S. Panasenko
We consider some recently constructed examples of simple finite-dimensional right-alternative superalgebras and right-symmetric algebras. We prove that the central order in any of…
Semiprime Novikov Algebras
A. S. Panasenko
We study prime and semiprime Novikov algebras. We prove that prime nonassociative Novikov algebra has zero nucleus and center. It is well known that an ideal of an alternative (sem…
Defining relations and Gröbner--Shirshov bases of Poisson algebras as of conformal modules
P. S. Kolesnikov, A. S. Panasenko
We study the relation between Poisson algebras and representations of Lie conformal algebras. We establish a setting for the calculation of a Gröbner--Shirshov basis in a module ov…
Central orders in simple finite dimensional superalgebras
A. S. Panasenko
The well-known Formanek's module finiteness theorem states that every unital prime PI-algebra (i.e. a central order in a matrix algebra by Posner's theorem) embeds into a finitely…