All intra-regular generalized hypersubstitutions of type (2)

Ampika Boonmee; Sorasak Leeratanavalee

doi:10.2478/ausm-2019-0003

All intra-regular generalized hypersubstitutions of type (2)

Acta Universitatis Sapientiae Mathematica ◽

10.2478/ausm-2019-0003 ◽

2019 ◽

Vol 11 (1) ◽

pp. 29-39

Author(s):

Ampika Boonmee ◽

Sorasak Leeratanavalee

Keyword(s):

Operation Symbol ◽

Regular Elements

Abstract A generalized hypersubstitution of type τ maps each operation symbol of the type to a term of the type, and can be extended to a mapping defined on the set of all terms of this type. The set of all such generalized hypersubstitutions forms a monoid. An element a of a semigroup S is intra-regular if there is b ∈ S such that a = baab. In this paper, we determine the set of all intra-regular elements of this monoid for type τ = (2).

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Green’s Relations on Regular Elements of Semigroup of Relational Hypersubstitutions for Algebraic Systems of Type ((m), (n))

Tamkang Journal of Mathematics ◽

10.5556/j.tkjm.53.2022.3436 ◽

2021 ◽

Vol 53 ◽

Author(s):

Sorasak Leeratanavalee ◽

Jukkrit Daengsaen

Keyword(s):

Green’S Relations ◽

Operation Symbol ◽

Algebraic Systems ◽

Regular Elements ◽

Relational Term ◽

Green's Relations ◽

Algebraic Properties

Any relational hypersubstitution for algebraic systems of type (τ,τ′) = ((mi)i∈I,(nj)j∈J) is a mapping which maps any mi-ary operation symbol to an mi-ary term and maps any nj - ary relational symbol to an nj-ary relational term preserving arities, where I,J are indexed sets. Some algebraic properties of the monoid of all relational hypersubstitutions for algebraic systems of a special type, especially the characterization of its order and the set of all regular elements, were first studied by Phusanga and Koppitz[13] in 2018. In this paper, we study the Green’srelationsontheregularpartofthismonoidofaparticulartype(τ,τ′) = ((m),(n)), where m, n ≥ 2.

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All idempotent and regular elements in the monoid of generalized hypersubstitutions for algebraic systems of type (2; 2)

Asian-European Journal of Mathematics ◽

10.1142/s1793557121500157 ◽

2019 ◽

pp. 2150015

Author(s):

D. Phusanga ◽

J. Joomwong ◽

S. Jino ◽

J. Koppitz

Keyword(s):

The Other ◽

Algebraic Systems ◽

General Algebra ◽

Regular Elements ◽

Other Hand

There are two different concepts for hypersubstitutions for algebraic systems [K. Denecke and D. Phusanga, Hyperformulas and solid algebraic systems, Studia Logica 90(2) (2008) 263–286; J. Koppitz and D. Phusanga, The monoid of hypersubstitutions for algebraic systems, J. Announcements Union Sci. Sliven 33(1) (2018) 120–127]. In this paper, we follow the more natural and practicable one given in [J. Koppitz and D. Phusanga, The monoid of hypersubstitutions for algebraic systems, J. Announcements Union Sci. Sliven 33(1) (2018) 120–127]. On the other hand, in [S. Leeratanavalee and K. Denecke, Generalized hypersubstitutions and strongly solid varieties, General Algebra and Applications[Formula: see text] Proc. of 59th Workshop on General Algebra[Formula: see text] 15th Conf. for Young Algebraists Potsdam 2000 (Shaker Verlag, 2000), pp. 135–145], the concept of the monoid of generalized hypersubstitutions was introduced. Following both ideas, one obtains the concept of a monoid of generalized hypersubstitutions for algebraic systems in a canonical way. The purpose of this paper is the study of the monoid of generalized hypersubstitutions for algebraic systems. We characterize the idempotent as well as regular elements in this monoid.

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