V. Drensky

collaborators

6 papers

math.RA2026

Central polynomials of minimal degree for matrices

Vesselin Drensky, Boyan Kostadinov

Formanek made the conjecture that the minimal degree of the central polynomials for the $n \times n$ matrix algebra over a field of characteristic 0 is $(n^{2} + 3 n - 2) /2$ and this is tr…

math.RA2026

Varieties of bicommutative algebras with identity of degree three

Vesselin Drensky, Bekzat Zhakhayev

The variety of bicommutative algebras is the class of all nonassociative algebras satisfying the polynomial identities $(x_{1} x_{2}) x_{3} = (x_{1} x_{3}) x_{2}$ and $x_{1} (x_{2} x_{3}) = x_{2} (x_{1} x_{3})$ . In t…

math.RA2026

Finite basis problem for varieties of algebraic systems

Vesselin Drensky

This is a survey on the finite basis problem for varieties of algebraic systems. Our exposition is in two directions: (i) We give numerous examples of varieties which are not finit…

math.RA2026

On cyclic invariants of the free associative algebra

Silvia Boumova, Vesselin Drensky

Let $K ⟨ X_{d} ⟩$ be the free associative algebra of rank $d \geq 2$ over a field $K$ . Lane in 1976 and Kharchenko in 1978 proved that the algebra of invariants $K\langle X…

math.RA2026

On dihedral invariants of the free associative algebra of rank two

Silvia Boumova, Vesselin Drensky, Åehmus FÄ±ndÄ±k

Let $K ⟨ X_{d} ⟩$ denote the free associative algebra of rank $d \geq 2$ over a field $K$ . By results of Lane (1976) and Kharchenko (1978), the algebra of invariants $K\lan…

math.RA2026

Varieties of associative algebras with an identity of third degree

Lyubov A. Vladimirova, Vesselin S. Drensky

We give a complete description of the varieties of associative algebras over a field of characteristic zero which satisfy a polynomial identity of third degree.