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    Wyświetlanie 1-6 z 6
    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
    Tytuł:
    T-Varieties and Clones of T-terms
    Autorzy:
    Denecke, Klaus
    Jampachon, Prakit
    Powiązania:
    https://bibliotekanauki.pl/articles/729099.pdf
    Data publikacji:
    2005
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    T-quasi constant algebra
    T-identity
    j-ideal
    T-hyperidentity
    clone of T-terms
    Opis:
    The aim of this paper is to describe how varieties of algebras of type τ can be classified by using the form of the terms which build the (defining) identities of the variety. There are several possibilities to do so. In [3], [19], [15] normal identities were considered, i.e. identities which have the form x ≈ x or s ≈ t, where s and t contain at least one operation symbol. This was generalized in [14] to k-normal identities and in [4] to P-compatible identities. More generally, we select a subset T of $W_{τ}(X)$, the set of all terms of type τ, and consider identities from T×T. Since any variety can be described by one heterogenous algebra, its clone, we are also interested in the corresponding clone-like structure. Identities of the clone of a variety V correspond to M-hyperidentities for certain monoids M of hypersubstitutions. Therefore we will also investigate these monoids and the corresponding M-hyperidentities.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2005, 25, 1; 89-101
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Axiomatization of quasigroups
    Autorzy:
    Smith, Jonathan
    Powiązania:
    https://bibliotekanauki.pl/articles/729131.pdf
    Data publikacji:
    2006
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    quasigroup
    heterogeneous algebra
    hyperidentity
    Opis:
    Quasigroups were originally described combinatorially, in terms of existence and uniqueness conditions on the solutions to certain equations. Evans introduced a universal-algebraic characterization, as algebras with three binary operations satisfying four identities. Now, quasigroups are redefined as heterogeneous algebras, satisfying just two conditions respectively known as hypercommutativity and hypercancellativity.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2007, 27, 1
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Hyperidentities in many-sorted algebras
    Autorzy:
    Denecke, Klaus
    Lekkoksung, Somsak
    Powiązania:
    https://bibliotekanauki.pl/articles/728740.pdf
    Data publikacji:
    2009
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    hypersubstitution
    hyperidentity
    heterogeneous algebra
    Opis:
    The theory of hyperidentities generalizes the equational theory of universal algebras and is applicable in several fields of science, especially in computers sciences (see e.g. [2,1]). The main tool to study hyperidentities is the concept of a hypersubstitution. Hypersubstitutions of many-sorted algebras were studied in [3]. On the basis of hypersubstitutions one defines a pair of closure operators which turns out to be a conjugate pair. The theory of conjugate pairs of additive closure operators can be applied to characterize solid varieties, i.e., varieties in which every identity is satisfied as a hyperidentity (see [4]). The aim of this paper is to apply the theory of conjugate pairs of additive closure operators to many-sorted algebras.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2009, 29, 1; 47-74
    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:
    All regular-solid varieties of idempotent semirings
    Autorzy:
    Hounnon, Hippolyte
    Powiązania:
    https://bibliotekanauki.pl/articles/38114594.pdf
    Data publikacji:
    2017-06-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    semiring
    hypersubstitution
    regular hypersubstitution
    regular hyperidentity
    solid variety
    regular-solid variety
    Opis:
    The lattice of all regular-solid varieties of semirings splits in two complete sublattices: the sublattice of all idempotent regular-solid varieties of semirings and the sublattice of all normal regular-solid varieties of semirings. In this paper, we discuss the idempotent part.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2017, 37, 1; 5-12
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-6 z 6

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