Regularity of Relational Hypersubstitutions for Algebraic Systems

Daengsaen, Jukkrit; Leeratanavalee, Sorasak

doi:10.17654/nt044020229

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2021

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“…Then the structure Relhyp(τ, τ ′ ) = (Relhyp(τ, τ ′ ), • h , σ id ) forms a monoid. In [3], the authors studied the regularity of relational hypersubstitution for algebraic systems of type ((m), (n)). In this paper, we study the Green's relations on the set of all regular relational hypersubstitutions for algebraic systems of type ((m), (n)), for arbitrary natural numbers m, n ≥ 2.…”

Section: Introductionmentioning

confidence: 99%

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

Leeratanavalee¹,

Daengsaen²

2021

Tamkang J. Math.

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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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Section: Introductionmentioning

confidence: 99%