On Partial Clones of k-terms

Lekkoksung, Nareupanat; Lekkoksung, Somsak

doi:10.7151/dmgaa.1376

Cited by 4 publications

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“…It turns out that clone(τ ) satisfies the axioms (C1)-(C3), and hence it belongs to the variety K 0 . Current topics in the construction of new terms have been extensively studied, for example, linear terms [9] and their extensions [25], full terms induced by order-decreasing transformations [34] and terms with a fixed variable [33]. Stable varieties of semigroups characterized by terms were obtained in [30].…”

Section: T Kumduang and S Leeratanavaleementioning

confidence: 99%

The partial many-sorted algebras of terms and formulas with fixed variables count

Leeratanavalee,

Kumduang

2023

Discuss. Math. - General Algebra and Applications

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Terms and formulas, which are formal expressions in first and second order languages obtained by alphabets, operation symbols, and relation symbols, are used to study algebras and algebraic systems. In this paper, we introduce the notion of terms with fixed variables count. The partial manysorted superposition operations of such terms and their partial many-sorted algebra satisfying clone axioms as weak identities are presented. We also extend our structures from algebras to algebraic systems via the concept of formulas with fixed variables count. Conditions for the set of such formulas to be closed under taking of superposition of formulas are determined. We construct the partial many-sorted algebra of formulas with fixed variables count and investigate its satisfaction by clone axioms. Finally, we prove that such partial structure is isomorphic to some Menger systems of the same rank of partial multiplace functions.

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Section: T Kumduang and S Leeratanavaleementioning

confidence: 99%

The partial many-sorted algebras of terms and formulas with fixed variables count

Leeratanavalee,

Kumduang

2023

Discuss. Math. - General Algebra and Applications

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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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Superassociative structures of terms and formulas defined by transformations preserving a partition

Kumduang

Sriwongsa

2023

Communications in Algebra

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On Partial Clones of k-terms

Cited by 4 publications

References 0 publications

The partial many-sorted algebras of terms and formulas with fixed variables count

The partial many-sorted algebras of terms and formulas with fixed variables count

Algebras of full terms constructed from transformations with fixed set

Superassociative structures of terms and formulas defined by transformations preserving a partition

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