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Hyperidentities in associative graph algebras

100%

Poomsa-ard T.

Discussiones Mathematicae - General Algebra and Applications

2000

tom 20

nr 2

169-182

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 by any term operations of A of the appropriate arity, the resulting identities hold in A. In this paper we characterize associative graph algebras, identities in associative graph algebras and hyperidentities in associative graph algebras.

The Galois correspondence between subvariety lattices and monoids of hpersubstitutions

63%

Denecke K., Hyndman J., Wismath S.

Discussiones Mathematicae - General Algebra and Applications

2000

tom 20

nr 1

21-36

Denecke and Reichel have described a method of studying the lattice of all varieties of a given type by using monoids of hypersubstitutions. In this paper we develop a Galois correspondence between monoids of hypersubstitutions of a given type and lattices of subvarieties of a given variety of that type. We then apply the results obtained to the lattice of varieties of bands (idempotent semigroups), and study the complete sublattices of this lattice obtained through the Galois correspondence.

Ograniczanie wyników

2 Discussiones Mathematicae - General Algebra and Applications

1 Denecke K.

1 Hyndman J.

1 Poomsa-ard T.

1 Wismath S.

2 2000

Wyniki wyszukiwania

Hyperidentities in associative graph algebras

The Galois correspondence between subvariety lattices and monoids of hpersubstitutions