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Hyperidentities in transitive graph algebras

100%

Poomsa-ard T., Wetweerapong J., Samartkoon C.

Discussiones Mathematicae - General Algebra and Applications

2005

tom 25

nr 1

23-37

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 in s and t are replaced by any term operations of A of the appropriate arity, the resulting identities hold in A̲ . In this paper we characterize transitive graph algebras, identities and hyperidentities in transitive graph algebras.

Special m-hyperidentities in biregular leftmost graph varieties of type (2,0)

84%

Anantpinitwatna A., Poomsa-ard T.

Discussiones Mathematicae - General Algebra and Applications

2009

tom 29

nr 2

81-107

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 a term equation s ≈ t if the corresponding graph algebra $\underline{A(G)}$ satisfies s ≈ t. A class of graph algebras V is called a graph variety if $V = Mod_g Σ$ where Σ is a subset of T(X) × T(X). A graph variety $V' = Mod_gΣ'$ is called a biregular leftmost graph variety if Σ' is a set of biregular leftmost term equations. A term equation s ≈ t is called an identity in a variety V if $\underline{A(G)}$ satisfies s ≈ t for all G ∈ V. An identity s ≈ t of a variety V is called a hyperidentity of a graph algebra $\underline{A(G)}$, G ∈ V whenever the operation symbols occuring in s and t are replaced by any term operations of $\underline{A(G)}$ of the appropriate arity, the resulting identities hold in $\underline{A(G)}$. An identity s ≈ t of a variety V is called an M-hyperidentity of a graph algebra $\underline{A(G)}$, G ∈ V whenever the operation symbols occuring in s and t are replaced by any term operations in a subgroupoid M of term operations of $\underline{A(G)}$ of the appropriate arity, the resulting identities hold in $\underline{A(G)}$. In this paper we characterize special M-hyperidentities in each biregular leftmost graph variety. For identities, varieties and other basic concepts of universal algebra see e.g. [3].

Ograniczanie wyników

2 Discussiones Mathematicae - General Algebra and Applications

2 Poomsa-ard T.

1 Anantpinitwatna A.

1 Samartkoon C.

1 Wetweerapong J.

1 2009

1 2005

Wyniki wyszukiwania

Hyperidentities in transitive graph algebras

Special m-hyperidentities in biregular leftmost graph varieties of type (2,0)