Universal algebra


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universal algebra

[¦yü·nə¦vər·səl ′al·jə·brə]
(mathematics)
The study of algebraic systems such as groups, rings, modules, and fields and the examination of what families of theorems are analogous in each system.

Universal algebra

(logic)
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References in periodicals archive ?
The choice of allowable representations affects the corresponding universal algebra, they say, and they seek quite general conditions that allow them to show that the C*-envelope of the semicrossed product is (a full corner of) a crossed product of an auxiliary C*-algebra by a group action.
For partial representations of Hopf algebras, there is also a universal algebra factorizing partial representations by algebra morphisms and this algebra has the structure of a Hopf algebroid.
This suggests that perhaps those results could be obtained in a uniform way that is similar to how universal algebra gives a framework for studying algebraic structures.
Our main tools come from Stone duality in various forms including the Jonsson-Tarski canonical extensions and profinite algebra, and from universal algebra and category theory.
These objects allow us to build in a combinatorial way a universal algebra which projects on Hecke algebra of ([S.
He also helps those needing a better understanding of categorical concepts, universal algebra and coalgebras in appendices and provides comprehensive references.
His earliest writings were A Treatise on Universal Algebra (1898), The Axioms of Projective Geometry (1906), The Axioms of Descriptive Geometry (1907), and An Introduction to Mathematics (1911).
Objective: As noted by T Y Lam in his book, A first course in noncommutative rings, noncommutative ring theory is a fertile meeting ground for group theory (group rings), representation theory (modules), functional analysis (operator algebras), Lie theory (enveloping algebras), algebraic geometry (finitely generated algebras, differential operators), noncommutative algebraic geometry (graded domains), arithmetic (orders, Brauer groups), universal algebra (co-homology of rings, projective modules) and quantum physics (quantum matrices).
In these proceedings from the conference of June 2001, participants describe their experience and research in developing graphs and patterns in such areas as Feynman diagrams (including in Hopf algebras and symmetries), algebraic structures (such as universal algebra, differential equations in noncommutative calculus, and twisted chiral de Rham algebras), manifolds, invariants and mirror symmetry (as in tri-level variants of three-folds, Massey products and the Johnson homomorphism), combinatorial aspects of dynamics (such as extensions, quotients and generalized pseudo-Anosov maps), and physics (such as in applications to study of black holes and the big bang).
The existence of both the universal enveloping algebra and the restricted universal enveloping algebra is to be expected by the general principles of universal algebra.
Gratzer, Two Mal'cev type theorems in universal algebra, J.
Since differential (R, e)-algebras form a variety of universal algebras, this and what we say in Example 1.

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