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- Rota-Baxter type operators, rewriting systems and Gröbner-Shirshov bases
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Differential type operators and Gröbner-Shirshov bases
A long standing problem of Gian-Carlo Rota for associative algebras is the classification of all linear operators that can be defined on them. In the 1970s, there were only a few known operators, for example, the derivative operator, the difference ...
Monomial Orderings, Rewriting Systems, and Gröbner Bases for the Commutator Ideal of a Free Algebra
In this paper we consider a free associative algebra on three generators over an arbitrary fieldK. Given a term ordering on the commutative polynomial ring on three variables overK, we construct uncountably many liftings of this term ordering to a ...
Construction of free differential algebras by extending Gröbner-Shirshov bases
AbstractAs a fundamental notion, the free differential algebra on a set is concretely constructed as the polynomial algebra on the differential variables. Such a construction is not known for the more general notion of the free differential ...
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