Composition-Diamond Lemma for Non-associative Algebras over a Commutative Algebra

Abstract

We establish the Composition-Diamond lemma for non-associative algebras over a free commutative algebra. As an application, we prove that every countably generated non-associative algebra over an arbitrary commutative algebra $K$ can be embedded into a two-generated non-associative algebra over $K$.Comment: 10 page