2 papers
math.RA2026
A Nielsen--Schreier variety of algebras without the PBW property
Vladimir Dotsenko, Bekzat Zhakhayev
We prove the Nielsen--Schreier property for the variety of algebras defined by the identity : every subalgebra of every free algebra in this variety is itself fr…
math.RA2025
Derived operations satisfy standard identities
Vladimir Dotsenko
A derived operation is a bilinear operation on a commutative associative algebra defined intrinsically out of its product and several derivations of the product. We show that o…