Definition for "Variety (Universal Algebra)" in the Quantum Dictionary

- Mathematics & Logic -

Pure Mathematics Dictionary

A variety in universal algebra is a class of algebras of the same signature closed under homomorphic images (H), subalgebras (S), and arbitrary direct products (P); equivalently, a class axiomatizable by a set of identities (equations).

- Pure Mathematics -

Algebra Dictionary

A class of algebras of a fixed signature that is closed under homomorphic images, subalgebras, and arbitrary direct products; equivalently, the class of all models satisfying a given set of algebraic identities (equations).