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IDEMPOTENT RANK IN THE ENDOMORPHISM MONOID OF A NONUNIFORM PARTITION

Part of: Semigroups

Published online by Cambridge University Press:  10 August 2015

IGOR DOLINKA ,
JAMES EAST  and
JAMES D. MITCHELL
IGOR DOLINKA
Affiliation:
Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21101 Novi Sad, Serbia email dockie@dmi.uns.ac.rs
JAMES EAST*
Affiliation:
Centre for Research in Mathematics, School of Computing, Engineering and Mathematics, University of Western Sydney, Locked Bag 1797, Penrith, NSW 2751, Australia email J.East@uws.edu.au
JAMES D. MITCHELL
Affiliation:
Mathematical Institute, School of Mathematics and Statistics, University of St Andrews, St Andrews, Fife, KY16 9SS, UK email jdm3@st-and.ac.uk
*
✉J.East@uws.edu.au
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Abstract

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We calculate the rank and idempotent rank of the semigroup ${\mathcal{E}}(X,{\mathcal{P}})$ generated by the idempotents of the semigroup ${\mathcal{T}}(X,{\mathcal{P}})$ which consists of all transformations of the finite set $X$ preserving a nonuniform partition ${\mathcal{P}}$. We also classify and enumerate the idempotent generating sets of minimal possible size. This extends results of the first two authors in the uniform case.

Keywords

transformation semigroupsidempotentsgeneratorsrankidempotent rank

MSC classification

Primary: 20M20: Semigroups of transformations, etc.
Secondary: 20M17: Regular semigroups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 93 , Issue 1 , February 2016 , pp. 73 - 91
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

References

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