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How algebraic is algebra?

Adámek, Jiří, Lawvere, F.W., Rosický, Jiří (2001)

Theory and Applications of Categories [electronic only]

Hu's Primal Algebra Theorem revisited

Hans-Eberhard Porst (2000)

Commentationes Mathematicae Universitatis Carolinae

It is shown how Lawvere's one-to-one translation between Birkhoff's description of varieties and the categorical one (see [6]) turns Hu's theorem on varieties generated by a primal algebra (see [4], [5]) into a simple reformulation of the classical representation theorem of finite Boolean algebras as powerset algebras.

Hyperidentities in associative graph algebras

Tiang Poomsa-ard (2000)

Discussiones Mathematicae - General Algebra and Applications

Graph algebras establish a connection between directed graphs without multiple edges and special universal algebras of type (2,0). We say that a graph G satisfies an identity s ≈ t if the correspondinggraph algebra A(G) satisfies s ≈ t. A graph G is called associative if the corresponding graph algebra A(G) satisfies the equation (xy)z ≈ x(yz). An identity s ≈ t of terms s and t of any type τ is called a hyperidentity of an algebra A̲ if whenever the operation symbols occurring in s and t are replaced...

Hyperidentities in many-sorted algebras

Klaus Denecke, Somsak Lekkoksung (2009)

Discussiones Mathematicae - General Algebra and Applications

The theory of hyperidentities generalizes the equational theory of universal algebras and is applicable in several fields of science, especially in computers sciences (see e.g. [2,1]). The main tool to study hyperidentities is the concept of a hypersubstitution. Hypersubstitutions of many-sorted algebras were studied in [3]. On the basis of hypersubstitutions one defines a pair of closure operators which turns out to be a conjugate pair. The theory of conjugate pairs of additive closure operators...

Hyperidentities in transitive graph algebras

Tiang Poomsa-ard, Jeerayut Wetweerapong, Charuchai Samartkoon (2005)

Discussiones Mathematicae - General Algebra and Applications

Graph algebras establish a connection between directed graphs without multiple edges and special universal algebras of type (2,0). We say that a graph G satisfies an identity s ≈ t if the corresponding graph algebra A(G) satisfies s ≈ t. A graph G = (V,E) is called a transitive graph if the corresponding graph algebra A(G) satisfies the equation x(yz) ≈ (xz)(yz). An identity s ≈ t of terms s and t of any type t is called a hyperidentity of an algebra A̲ if whenever the operation symbols occurring...

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