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Wyświetlanie 1-3 z 3
Tytuł:
Hyperidentities in associative graph algebras
Autorzy:
Poomsa-ard, Tiang
Powiązania:
https://bibliotekanauki.pl/articles/728812.pdf
Data publikacji:
2000
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
identities
hyperidentities
associative graph algebras
terms
Opis:
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.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2000, 20, 2; 169-182
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Special m-hyperidentities in biregular leftmost graph varieties of type (2,0)
Autorzy:
Anantpinitwatna, Apinant
Poomsa-ard, Tiang
Powiązania:
https://bibliotekanauki.pl/articles/728744.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
varieties
biregular leftmost graph varieties
identities
term
hyperidentity
M-hyperidentity
binary algebra
graph algebra
Opis:
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].
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2009, 29, 2; 81-107
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Hyperidentities in transitive graph algebras
Autorzy:
Poomsa-ard, Tiang
Wetweerapong, Jeerayut
Samartkoon, Charuchai
Powiązania:
https://bibliotekanauki.pl/articles/729103.pdf
Data publikacji:
2005
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
identity
hyperidentity
term
normal form term
binary algebra
graph algebra
transitive graph algebra
Opis:
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.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2005, 25, 1; 23-37
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
    Wyświetlanie 1-3 z 3

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