Semigroups of Terms, Tree Languages, Menger Algebra of n-Ary Functions and Their Embedding Theorems

Kumduang, Thodsaporn; Leeratanavalee, Sorasak

doi:10.3390/sym13040558

Cited by 5 publications

(4 citation statements)

References 17 publications

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“…Stable varieties of semigroups characterized by terms were obtained in [30]. Furthermore, a mapping whose range is the set of different kinds of terms was presented in [5,22,23].…”

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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“…Stable varieties of semigroups characterized by terms were obtained in [30]. Furthermore, a mapping whose range is the set of different kinds of terms was presented in [5,22,23].…”

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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“…In addition, a superassociative system of n-ary operation is one of the popular subject for studying the algebraic structural properties of n-ary functions in this recently decade. For further results on this direction, see [7,15,26].…”

Section: Introductionmentioning

confidence: 99%

Fuzzy ideals and fuzzy congruences on menger algebras with their homomorphism properties

Kumduang¹,

Chinram²

2023

Discuss. Math. - General Algebra and Applications

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It is well known that Menger algebras, sometime called superassociative algebras, play a major role in both mathematical sciences and related areas. The notion of fuzzy sets was initiated by L.A. Zadeh as a general mathematical machinery of classical sets. The present paper establishes a strong interaction between fuzzy sets and Menger algebras. We show that the set of all fuzzy subsets on G together with one (n + 1)-ary operation forms a Menger algebra. The concepts of several kinds of fuzzy ideals in Menger algebras are introduced and some related properties are investigated. Furthermore, we provide a construction of quotient Menger algebras via fuzzy congruence relations. Finally, homomorphism theorems in terms of fuzzy congruences are studied. Our results can be considered as a generalization in the study of semigroup theory too.

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“…These sets are examples of tree languages over the terms from W (3) (X). In 2021, tree languages with fixed variables which can be considered as one of particular classes of tree languages were presented in [17]. We mentioned that tree languages generalize formal languages, i.e., sets of words over a given alphabet.…”

Section: Introduction and Basic Propertiesmentioning

confidence: 99%

Algebras of generalized tree languages with fixed variables

Phuapong,

Chansuriya,

Kumduang

2023

ADM

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Tree languages which are sets of terms always play a prominent role in the first-order languages and theoretical computer science. In this paper, tree languages induced by terms with fixed variables are considered. Under the applications of an operation on tree languages, we construct the algebra of such languages having many properties of abstract clones. A strong connection with theory of general functions is given through a representation theorem. Additionally, the semigroup of mappings of which their images are tree languages with fixed variables is given.

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Semigroups of Terms, Tree Languages, Menger Algebra of n-Ary Functions and Their Embedding Theorems

Cited by 5 publications

References 17 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

Fuzzy ideals and fuzzy congruences on menger algebras with their homomorphism properties

Algebras of generalized tree languages with fixed variables

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