Universal algebra is the field of mathematics that studies algebraic structures in general rather than any one specific type of structure. Rather than studying groups or rings as such, which is the work of group theory and ring theory, universal algebra studies the possible types of algebraic structures and the relationships among them.
Facts
Central QuestionRather than studying one particular kind of algebraic structure such as groups or rings, universal algebra asks what general operations, properties and relationships hold across algebraic structures of every type. 1 Key DebateWho actually founded universal algebra as a field is a matter of record rather than agreement: Alfred North Whitehead named the subject and set out its comparative program in 1898, crediting Hamilton, De Morgan and Sylvester as originators, but by the article's own account he produced no general results, and the subject did not become an active research field until Garrett Birkhoff and Oystein Ore began publishing on it in the early 1930s. 1 Classification
Pure or Applied Connections
Associated With
Source Universal Algebra (Wikipedia)
Sources
1. Universal Algebra (Wikipedia)
Wikimedia FoundationLead section
Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures in general, not specific types of algebraic structures.
History section
Whitehead, however, had no results of a general nature. Work on the subject was minimal until the early 1930s, when Garrett Birkhoff and Øystein Ore began publishing on universal algebras.
Associated With: Algebra, Wikipedia lead paragraph, Universal algebra
Universal algebra is the field of mathematics that studies algebraic structures in general, not specific types of algebraic structures.
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