All 2-potent Elements in HypG(2)

Authors

  • Apatsara Sareeto Master's Degree Program in Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200
  • Sorasak Leeratanavalee Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200

DOI:

https://doi.org/10.26713/cma.v11i2.1332

Keywords:

Generalized hypersubstitution, m-potent elements, 2-potent elements

Abstract

A generalized hypersubstitution of type τ=(2) is a function which takes the binary operation symbol f to the term σ(f) which does not necessarily preserve the arity. Let HypG(2) be the set of all these generalized hypersubstitutions of type (2). The set HypG(2) with a binary operation and the identity generalized hypersubstitution forms a monoid. The index and period of an element a of a finite semigroup are the smallest values of m≥1 and r≥1 such that am+r=am. An element with the index m and period 1 is called an $m$-potent element. In this paper we determine all 2-potent elements in HypG(2).

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References

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Published

30-06-2020
CITATION

How to Cite

Sareeto, A., & Leeratanavalee, S. (2020). All 2-potent Elements in HypG(2). Communications in Mathematics and Applications, 11(2), 221–232. https://doi.org/10.26713/cma.v11i2.1332

Issue

Vol. 11 No. 2 (2020)

Section

Research Article

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