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REGULAR ELEMENTS AND GREEN'S RELATIONS IN POWER MENGER ALGEBRAS OF TERMS

REGULAR ELEMENTS AND GREEN'S RELATIONS IN POWER MENGER ALGEBRAS OF TERMS DEMONSTRATIO MATHEMATICAVol. XLINo 12008K . Denecke, P. GlubudomR E G U L A R ELEMENTS AND GREEN'S RELATIONSIN P O W E R M E N G E R A L G E B R A S OF T E R M SAbstract. Sets of terms of type r are called tree languages (see [5]). On sets of treelanguages superposition operations can be defined in such a way that the collection of alltree languages of type r forms an abstract clone. Considering only sets of n-ary termsone obtains a Menger algebra (see e.g. [3]). From the superposition operations binaryoperations on tree languages can be derived. For the corresponding semigroups of treelanguages we study idempotent and regular elements as well as Green's relations C and 1Z.1. I n t r o d u c t i o nWe consider an indexed set of operation symbols /¿, where fa is n^-aryfor every i G / , and a finite alphabet Xn : = { x i , . . .Let r : = (nj)i e /be the sequence of all these arities. This sequence r is called the type ofthe terms. Then the set WT(Xn) of all n-ary terms of type http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

REGULAR ELEMENTS AND GREEN'S RELATIONS IN POWER MENGER ALGEBRAS OF TERMS

Denecke, K.; Glubudom, P.
Demonstratio Mathematica , Volume 41 (1): 12 – Jan 1, 2008
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References (12)

Publisher
de Gruyter
Copyright
© by K. Denecke
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-2008-0103
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHEMATICAVol. XLINo 12008K . Denecke, P. GlubudomR E G U L A R ELEMENTS AND GREEN'S RELATIONSIN P O W E R M E N G E R A L G E B R A S OF T E R M SAbstract. Sets of terms of type r are called tree languages (see [5]). On sets of treelanguages superposition operations can be defined in such a way that the collection of alltree languages of type r forms an abstract clone. Considering only sets of n-ary termsone obtains a Menger algebra (see e.g. [3]). From the superposition operations binaryoperations on tree languages can be derived. For the corresponding semigroups of treelanguages we study idempotent and regular elements as well as Green's relations C and 1Z.1. I n t r o d u c t i o nWe consider an indexed set of operation symbols /¿, where fa is n^-aryfor every i G / , and a finite alphabet Xn : = { x i , . . .Let r : = (nj)i e /be the sequence of all these arities. This sequence r is called the type ofthe terms. Then the set WT(Xn) of all n-ary terms of type

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Demonstratio Mathematica – de Gruyter

Published: Jan 1, 2008

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