Autor: Changphas, Thawhat - Prolib Integro

Skocz do pozycji: 1.

Tytuł:: The Clone of K*(n, r)-Full Terms
Autorzy:: Wattanatripop, Khwancheewa
Changphas, Thawhat
Tematy:: restricted range transformation
full term
clone
Menger algebra
hypersubstitution
hyperidentity
solid variety; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/55795293.pdf Link otwiera się w nowym oknie
Opis:: Let τ_n be a type of algebras in which all operation symbols have arity n, for a fixed n ≥ 1. For 0 < r ≤ n, this paper introduces a special kind of n-ary terms of type τ_n called K*(n, r)-full terms. The set of all K*(n, r)-full terms of type τ_n is closed under the superposition operation Sⁿ; hence forms a clone denoted by clone_K*(n,r)(τ_n). We prove that clone_{K* (n,r)}(τ_n) is a Menger algebra of rank n. We study K*(n, r)-full hypersubstitutions and the related K*(n, r)-full closed identities and K*(n, r)-full closed varieties. A connection between identities in clone_{K* (n,r)}(τ_n) and K*(n, r)-full closed identities is established. The results obtained generalize the results of Denecke and Jampachon [K. Denecke and P. Jampachon, Clones of full terms, Algebra and Discrete Math. 4 (2004) 1–11].
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Complexity of hypersubstitutions and lattices of varieties
Autorzy:: Changphas, Thawhat
Denecke, Klaus
Tematy:: hypersubstitution
left-seminearring
complexity ofa hypersubstitution
M-solid variety; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/728956.pdf Link otwiera się w nowym oknie
Opis:: Hypersubstitutions are mappings which map operation symbols to terms. The set of all hypersubstitutions of a given type forms a monoid with respect to the composition of operations. Together with a second binary operation, to be written as addition, the set of all hypersubstitutions of a given type forms a left-seminearring. Monoids and left-seminearrings of hypersubstitutions can be used to describe complete sublattices of the lattice of all varieties of algebras of a given type. The complexity of a hypersubstitution can be measured by the complexity of the resulting terms. We prove that the set of all hypersubstitutions with a complexity greater than a given natural number forms a sub-left-seminearring of the left-seminearring of all hypersubstitutions of the considered type. Next we look to a special complexity measure, the operation symbol count op(t) of a term t and determine the greatest M-solid variety of semigroups where $M = H₂^{op}$ is the left-seminearring of all hypersubstitutions for which the number of operation symbols occurring in the resulting term is greater than or equal to 2. For every n ≥ 1 and for $M = Hₙ^{op}$ we determine the complete lattices of all M-solid varieties of semigroups.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: On nd-K*(n, r)-Full Hypersubstitutions
Autorzy:: Wattanatripop, Khwancheewa
Changphas, Thawhat
Tematy:: full term
nd-full hypersubstitution
K*(n, r)-full term
nd-K*(n, r)-full hypersubstitution; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/55795790.pdf Link otwiera się w nowym oknie
Opis:: Based on the notion of K*(n, r)-full terms defined by the authors, nd-K*(n, r)-full hypersubstitutions are defined. It turns out that the extension of an nd-K*(n, r)-full hypersubstitution is an endomorphism of the algebra of tree languages of nd-K*(n, r)-full terms.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 4.

Tytuł:: Algebras of full terms constructed from transformations with fixed set
Autorzy:: Wattanatripop, Khwancheewa
Changphas, Thawhat
Kumduang, Thodsaporn
Tematy:: transformations with fixed set
full term
Menger algebra
hypersubstitution
strongly full term
permutational full term; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/59498173.pdf Link otwiera się w nowym oknie
Opis:: Based on the notion of full transformations with fixed set, in this paper, we present a novel concept of $n$-ary $Fix(I_n,Y)$-full terms. This term can be considered as a generalization of strongly full terms, permutational full terms and full terms. Together with the superposition operation, one can form a Menger algebra of rank $n$. The freeness of such algebra with respect to a variety of algebras of the same types is discussed. Furthermore, we apply hypersubstitution theory to define a $Fix(I_n,Y)$-full closed identity, a $Fix(I_n,Y)$-full closed variety and present some concrete examples.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 5.

Tytuł:: Radicals of Generalized Prime Ideals in Ternary Semigroups
Autorzy:: Satvong, Narakon
Changphas, Thawhat
Luangchaisri, Panuwat
Tematy:: ternary semigroup
pseudo prime ideal
good mapping
f-prime ideal
left f-primary decomposition; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/55796410.pdf Link otwiera się w nowym oknie
Opis:: In this paper, the concepts of f-prime ideals and f-semiprime ideals on a ternary semigroup are considered as a generalization of pseudo prime ideals and pseudo semiprime ideals, respectively. Then such ideals introduced are used to describe left (respectively, right) f-primary ideals on a ternary semigroup.
Dostawca treści:: Biblioteka Nauki

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