Semigroups of an inductive composition of terms

Kitpratyakul, Pongsakorn; Pibaljommee, Bundit

doi:10.1142/s1793557122500383

Cited by 3 publications

(1 citation statement)

References 4 publications

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“…By W τn (X n ) we denote the set of all n-ary terms of type τ n . Recent contributions on terms can be found, for example, in [2,3,10,12,16]. Actually, in [5], K. Denecke and P.…”

Section: Introductionmentioning

confidence: 99%

Algebras of full terms constructed from transformations with fixed set

Kumduang,

Wattanatripop,

Changphas

2024

Discuss. Math. - General Algebra and Applications

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Based on th notion of full transformations with fixed set, in this paper, we present a novel concept of n-ary F ix(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 F ix(I n , Y )-full closed identity, a F ix(I n , Y )-full closed variety and present some concrete examples.

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“…By W τn (X n ) we denote the set of all n-ary terms of type τ n . Recent contributions on terms can be found, for example, in [2,3,10,12,16]. Actually, in [5], K. Denecke and P.…”

Section: Introductionmentioning

confidence: 99%

Algebras of full terms constructed from transformations with fixed set

Kumduang,

Wattanatripop,

Changphas

2024

Discuss. Math. - General Algebra and Applications

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On substructures of semigroups of inductive terms

Kitpratyakul¹,

Pibaljommee

2022

MATH

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<abstract><p>An inductive composition is an operation generalizing from a superposition $ S^n $ on the set of all $ n $-ary terms of type $ \tau $. A binary operation called <italic>inductive product</italic> is obtainable from such composition. It is a generalization of a tree language product but on the set of all $ n $-ary terms of type $ \tau $. Unlike the original one, this inductive product is not associative on the mentioned set. Nonetheless, it turns to be associative on some restricted set. A semigroup arising in this way is the main focus of this paper. We consider its special subsemigroups and semigroup factorizations.</p></abstract>

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Clones of inductive superpositions of terms

Kitpratyakul¹,

Pibaljommee

2023

MATH

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<abstract><p>A superposition is an operation of terms by which we substitute each variable within a term with other forms of terms. With more options of terms to be replaced, an inductive superposition is apparently more general than the superposition. This comes with a downside that it does not satisfy the superassociative property on the set of all terms of a given type while the superposition does. A derived base set of terms on which the inductive superposition is superassociative is given in this paper. A clone-like algebraic structure involving such base set and superposition is the main topic of this paper. Generating systems of the clone-like algebra are characterized and it turns out that the algebra is only free with respect to itself under the certain selections of fixed terms concerning its inductive superposition or the specific type of its base set.</p></abstract>

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Semigroups of an inductive composition of terms

Cited by 3 publications

References 4 publications

Algebras of full terms constructed from transformations with fixed set

Algebras of full terms constructed from transformations with fixed set

On substructures of semigroups of inductive terms

Clones of inductive superpositions of terms

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