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    Wyświetlanie 1-5 z 5
    Tytuł:
    Regular elements and Greens relations in Menger algebras of terms
    Autorzy:
    Denecke, Klaus
    Jampachon, Prakit
    Powiązania:
    https://bibliotekanauki.pl/articles/729175.pdf
    Data publikacji:
    2006
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    term
    superposition of terms
    Menger algebra
    regular element
    Green's relations
    Opis:
    Defining an (n+1)-ary superposition operation $S^n$ on the set $W_{τ}(X_n)$ of all n-ary terms of type τ, one obtains an algebra $n-clone τ := (W_{τ}(X_n); S^n, x_1, ..., x_n)$ of type (n+1,0,...,0). The algebra n-clone τ is free in the variety of all Menger algebras ([9]). Using the operation $S^n$ there are different possibilities to define binary associative operations on the set $W_{τ}(X_n)$ and on the cartesian power $W_{τ}(X_n)^n$. In this paper we study idempotent and regular elements as well as Green's relations in semigroups of terms with these binary associative operations as fundamental operations.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2006, 26, 1; 85-109
    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:
    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:
    Non-Deterministic Linear Hypersubstitutions
    Autorzy:
    Lekkoksung, Nareupanat
    Jampachon, Prakit
    Powiązania:
    https://bibliotekanauki.pl/articles/729155.pdf
    Data publikacji:
    2015
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    linear term
    non-deterministic linear hypersubstitution
    Opis:
    A non-deterministic hypersubstitution maps operation symbols to sets of terms of the corresponding arity. A non-deterministic hypersubstitution of type τ is said to be linear if it maps any operation symbol to a set of linear terms of the corresponding arity. We show that the extension of non-deterministic linear hypersubstitutions of type τ map sets of linear terms to sets of linear terms. As a consequence, the collection of all non-deterministic linear hypersubstitutions forms a monoid. Non-deterministic linear hypersubstitutions can be applied to identities and to algebras of type τ.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2015, 35, 1; 97-103
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Four-part semigroups - semigroups of Boolean operations
    Autorzy:
    Jampachon, Prakit
    Susanti, Yeni
    Denecke, Klaus
    Powiązania:
    https://bibliotekanauki.pl/articles/728987.pdf
    Data publikacji:
    2012
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    four-part semigroup
    Boolean operation
    Opis:
    Four-part semigroups form a new class of semigroups which became important when sets of Boolean operations which are closed under the binary superposition operation f + g := f(g,...,g), were studied. In this paper we describe the lattice of all subsemigroups of an arbitrary four-part semigroup, determine regular and idempotent elements, regular and idempotent subsemigroups, homomorphic images, Green's relations, and prove a representation theorem for four-part semigroups.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2012, 32, 1; 115-136
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-5 z 5

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