Generalized Gröbner bases and dimension polynomials of modules over some finitely generated noncommutative algebras

In this article the basic notions of a theory of Grobner bases for ideals in the non-associative, non-commutative algebra K{X} with a unit freely generated by a set X over a field K are discussed. The monomials in this algebra can be identified with the ...

We give a proof of the Poincaré-Birkhoff-Witt theorem for universal enveloping algebras of finite dimensional Leibniz algebras using Grobner bases in a free associative algebra. We also construct Gröbner bases for two-sided ideals in universal ...

We introduce a class of non-commutative polynomial rings over fields intermediate betweencommutative polynomial rings and general non-commutative polynomial rings. This class of solvable polynomial rings includes many rings arising naturally in ...