Universal Algebra

Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures themselves, not examples ("models") of algebraic structures. For instance, rather than take particular groups as the object of study, in universal algebra one takes "the theory of groups" as an object of study.

Read more about Universal AlgebraBasic Idea, Varieties, Basic Constructions, Some Basic Theorems, Motivations and Applications, History

Other articles related to "universal algebra, algebras, algebra":

Structure (mathematical Logic)
... In universal algebra and in model theory, a structure consists of a set along with a collection of finitary operations, and relations that are defined on it ... Universal algebra studies structures that generalize the algebraic structures such as groups, rings, fields and vector spaces ... The term universal algebra is used for structures with no relation symbols ...
Algebraic Structure - Universal Algebra
... Universal algebra abstractly studies such objects ... If all axioms defining a class of algebras are identities, then the class of objects is a variety (not to be confused with algebraic variety in the sense of algebraic geometry) ... The study of varieties is an important part of universal algebra ...
Garrett Birkhoff - Life
... physics but switched to studying abstract algebra under Philip Hall ... two important texts, Van der Waerden on abstract algebra and Speiser on group theory ... Mac Lane, substantially advanced American teaching and research in abstract algebra ...
Universal Algebra - History
... In Alfred North Whitehead's book A Treatise on Universal Algebra, published in 1898, the term universal algebra had essentially the same meaning that it has today ... At the time structures such as Lie algebras and hyperbolic quaternions drew attention to the need to expand algebraic structures beyond the associatively multiplicative class ... idea of the work is not unification of the several methods, nor generalization of ordinary algebra so as to include them, but rather the comparative study of their several structures." At the ...
Structure (mathematical Logic) - Other Generalizations - Partial Algebras
... Both universal algebra and model theory study classes of (structures or) algebras that are defined by a signature and a set of axioms ... The formalism of universal algebra is much more restrictive essentially it only allows first-order sentences that have the form of universally quantified equations between terms, e.g ... choice of a signature is more significant in universal algebra than it is in model theory ...

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