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Independence algebras, basis algebras and semigroups of quotients

Part of: Semigroups Algebraic structures

Published online by Cambridge University Press:  05 August 2010

Victoria Gould
Victoria Gould
Affiliation:
Department of Mathematics, University of York, Heslington, York YO10 5DD, UK ([email protected])
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Abstract

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We show that if A is a stable basis algebra satisfying the distributivity condition, then B is a reduct of an independence algebra A having the same rank. If this rank is finite, then the endomorphism monoid of B is a left order in the endomorphism monoid of A.

Keywords

semigroupindependencebasisexchange propertyendomorphism monoidquotients

MSC classification

Secondary: 20M20: Semigroups of transformations, etc. 08A35: Automorphisms, endomorphisms 20M10: General structure theory 08A05: Structure theory
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 53 , Issue 3 , October 2010 , pp. 697 - 729
Copyright
Copyright © Edinburgh Mathematical Society 2010

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