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    Wyświetlanie 1-6 z 6
    Tytuł:
    All completely regular elements in $Hyp_{G}(n)$
    Autorzy:
    Boonmee, Ampika
    Leeratanavalee, Sorasak
    Powiązania:
    https://bibliotekanauki.pl/articles/729081.pdf
    Data publikacji:
    2013
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    generalized hypersubstitution
    regular element
    completely regular element
    Opis:
    In Universal Algebra, identities are used to classify algebras into collections, called varieties and hyperidentities are use to classify varieties into collections, called hypervarities. The concept of a hypersubstitution is a tool to study hyperidentities and hypervarieties.
    Generalized hypersubstitutions and strong identities generalize the concepts of a hypersubstitution and of a hyperidentity, respectively. The set of all generalized hypersubstitutions forms a monoid. In this paper, we determine the set of all completely regular elements of this monoid of type τ=(n).
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2013, 33, 2; 211-219
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    All maximal completely regular submonoids of $Hyp_G(2)$
    Autorzy:
    Kunama, Pornpimol
    Leeratanavalee, Sorasak
    Powiązania:
    https://bibliotekanauki.pl/articles/38119704.pdf
    Data publikacji:
    2017-06-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    generalized hypersubstitution
    regular element
    completely regular
    Opis:
    In this paper we consider mappings σ which map the binary operation symbol f to the term σ (f) which do not necessarily preserve the arity. These mapping are called generalized hypersubstitutions of type τ = (2) and we denote the set of all these generalized hypersubstitutions of type τ = (2) by HypG(2). The set HypG(2) together with a binary operation defined on this set and the identity generalized hypersubstitution which maps f to the term f(x1, x2) forms a monoid. In this paper, we determine all maximal completely regular submonoids of this monoid.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2017, 37, 1; 105-114
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Idempotent Elements of Weak Projection Generalized Hypersubstitutions
    Autorzy:
    Lekkoksung, Nareupanat
    Jampachon, Prakit
    Powiązania:
    https://bibliotekanauki.pl/articles/52486380.pdf
    Data publikacji:
    2018-06-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    idempotent
    regular
    generalized hypersubstitution
    weak projection generalized hypersubstitution
    Opis:
    A generalized hypersubstitution of type τ = (ni)i∈I is a mapping σ which maps every operation symbol fi to the term σ(fi) and may not preserve arity. It is the main tool to study strong hyperidentities that are used to classify varieties into collections called strong hypervarieties. Each generalized hypersubstitution can be extended to a mapping σ̂ on the set of all terms of type τ. A binary operation on HypG(τ), the set of all generalized hypersubstitutions of type τ, can be defined by using this extension. The set HypG(τ) together with such a binary operation forms a monoid, where a hypersubstitution σid, which maps fi to fi(x1, . . ., xni) for every i ∈ I, is the neutral element of this monoid. A weak projection generalized hypersubstitution of type τ is a generalized hypersubstitution of type τ which maps at least one of the operation symbols to a variable. In semigroup theory, the various types of its elements are widely considered. In this paper, we present the characterizations of idempotent weak projection generalized hypersubstitutions of type (m, n) and give some sufficient conditions for a weak projection generalized hypersubstitution of type (m, n) to be regular, where m, n ≥ 1.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2018, 38, 1; 99-114
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    M-solid generalized non-deterministic varieties
    Autorzy:
    Lekkoksung, Somsak
    Powiązania:
    https://bibliotekanauki.pl/articles/728876.pdf
    Data publikacji:
    2016
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    generalized non-deterministic hypersubstitution
    conjugate pair of additive closure operators
    M-solid generalized non-deterministic variety
    Opis:
    A generalized non-deterministic hypersubstitution is a mapping which maps operation symbols of type τ to the set of terms of the same type which does not necessarily preserve the arity. We apply the generalized non-deterministic hypersubstitution to an algebra of type τ and obtain a class of derived algebras of type τ. The generalized non-deterministic hypersubstitutions can be also applied to sets of equations of type τ. We obtain two closure operators which turn out to be a conjugate pair of completely additive closure operators. This allows us to apply the theory of conjugate pairs of additive closure operators to characterize M-solid generalized non-deterministic varieties of algebras.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2016, 36, 1; 25-43
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Pre-strongly solid varieties of commutative semigroups
    Autorzy:
    Phuapong, Sarawut
    Leeratanavalee, Sorasak
    Powiązania:
    https://bibliotekanauki.pl/articles/728995.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    generalized hypersubstitution
    pre-strongly solid variety
    commutative semigroup
    Opis:
    Generalized hypersubstitutions are mappings from the set of all fundamental operations into the set of all terms of the same language do not necessarily preserve the arities. Strong hyperidentities are identities which are closed under the generalized hypersubstitutions and a strongly solid variety is a variety which every its identity is a strong hyperidentity. In this paper we give an example of pre-strongly solid varieties of commutative semigroups and determine the least and the greatest pre-strongly solid variety of commutative semigroups.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2011, 31, 1; 27-45
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The monoid of generalized hypersubstitutions of type τ = (n)
    Autorzy:
    Puninagool, Wattapong
    Leeratanavalee, Sorasak
    Powiązania:
    https://bibliotekanauki.pl/articles/729031.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    monoid
    regular elements
    idempotent elements
    Green's relations
    generalized hypersubstitution
    Opis:
    A (usual) hypersubstitution of type τ is a function which takes each operation symbol of the type to a term of the type, of the same arity. The set of all hypersubstitutions of a fixed type τ forms a monoid under composition, and semigroup properties of this monoid have been studied by a number of authors. In particular, idempotent and regular elements, and the Green's relations, have been studied for type (n) by S.L. Wismath.
    A generalized hypersubstitution of type τ=(n) is a mapping σ which takes the n-ary operation symbol f to a term σ(f) which does not necessarily preserve the arity. Any such σ can be inductively extended to a map σ̂ on the set of all terms of type τ=(n), and any two such extensions can be composed in a natural way. Thus, the set $Hyp_{G}(n)$ of all generalized hypersubstitutions of type τ=(n) forms a monoid. In this paper we study the semigroup properties of $Hyp_{G}(n)$. In particular, we characterize the idempotent and regular generalized hypersubstitutions, and describe some classes under Green's relations of this monoid.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2010, 30, 2; 173-191
    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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