Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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The Monoid of Linear Hypersubstitutions

  • Changphas, Thawhat (Department of Mathematics, Faculty of Science, Khon Kaen University) ;
  • Pibaljommee, Bundit (Department of Mathematics, Faculty of Science, Khon Kaen University) ;
  • Denecke, Klaus (Department of Mathematics, Faculty of Science, Khon Kaen University)
  • Received : 2018.08.22
  • Accepted : 2018.12.19
  • Published : 2019.12.23
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Abstract

A term is called linear if each variable which occurs in the term, occurs only once. A hypersubstitution is said to be linear if it maps any operation symbol to a linear term of the same arity. Linear hypersubstitutions have some importance in Theoretical Computer Science since they preserve recognizability [7]. We show that the collection of all linear hypersubstitutions forms a monoid. Linear hypersubstitutions are used to define linear hyperidentities. The set of all linear term operations of a given algebra forms with respect to certain superposition operations a function algebra. Hypersubstitutions define endomorphisms on this function algebra.

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References

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