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

Apinant Anantpinitwatna; Tiang Poomsa-ard

Discussiones Mathematicae - General Algebra and Applications (2009)

- Volume: 29, Issue: 2, page 81-107
- ISSN: 1509-9415

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topApinant Anantpinitwatna, and Tiang Poomsa-ard. "Special m-hyperidentities in biregular leftmost graph varieties of type (2,0)." Discussiones Mathematicae - General Algebra and Applications 29.2 (2009): 81-107. <http://eudml.org/doc/276824>.

@article{ApinantAnantpinitwatna2009,

abstract = {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 $V^\{\prime \} = Mod_gΣ^\{\prime \}$ 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].},

author = {Apinant Anantpinitwatna, Tiang Poomsa-ard},

journal = {Discussiones Mathematicae - General Algebra and Applications},

keywords = {varieties; biregular leftmost graph varieties; identities; term; hyperidentity; M-hyperidentity; binary algebra; graph algebra; -hyperidentity},

language = {eng},

number = {2},

pages = {81-107},

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

url = {http://eudml.org/doc/276824},

volume = {29},

year = {2009},

}

TY - JOUR

AU - Apinant Anantpinitwatna

AU - Tiang Poomsa-ard

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

JO - Discussiones Mathematicae - General Algebra and Applications

PY - 2009

VL - 29

IS - 2

SP - 81

EP - 107

AB - 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 $V^{\prime } = Mod_gΣ^{\prime }$ 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].

LA - eng

KW - varieties; biregular leftmost graph varieties; identities; term; hyperidentity; M-hyperidentity; binary algebra; graph algebra; -hyperidentity

UR - http://eudml.org/doc/276824

ER -

## References

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