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Hyperidentities in associative graph algebras

100%

Poomsa-ard T.

Discussiones Mathematicae - General Algebra and Applications

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2000

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tom 20

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nr 2

169-182

EN

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.

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

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Anantpinitwatna A., Poomsa-ard T.

Discussiones Mathematicae - General Algebra and Applications

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2009

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tom 29

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nr 2

81-107

EN

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].

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Hyperidentities in transitive graph algebras

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

Discussiones Mathematicae - General Algebra and Applications

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2005

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tom 25

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nr 1

23-37

EN

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.

Ograniczanie wyników

3 Discussiones Mathematicae - General Algebra and Applications

3 Poomsa-ard T.

1 Anantpinitwatna A.

1 Samartkoon C.

1 Wetweerapong J.

1 2009

1 2005

1 2000

Hyperidentities in associative graph algebras

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

Hyperidentities in transitive graph algebras