Variety (Universal Algebra)
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High Quality Content by WIKIPEDIA articles! In mathematics, specifically universal algebra, a variety of algebras is the class of all algebraic structures of a given signature satisfying a given set of identities. Equivalently, a variety is a class of algebraic structures of the same signature which is closed under the taking of homomorphic images, subalgebras and (direct) products. In the context of category theory, a variety of algebras is usually called a finitary algebraic category. A covariety is the class of all coalgebraic structures of a given signature. A variety of algebras should not be confused with an algebraic variety. Intuitively, a variety of algebras is an equationally defined collection of algebras, while an algebraic variety is an equationally defined collection of elements from a single algebra. The two are named alike by analogy, but they are formally quite distinct and their theories have little in common.
Herausgeber Lambert M. Surhone
Herausgeber Miriam T. Timpledon
Herausgeber Susan F. Marseken