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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
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
Corresponding
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Abstract

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.

Type
Research Article
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

References

Araújo, J., Bentz, W., Mitchell, J. D. and Schneider, C., ‘The rank of the semigroup of transformations stabilising a partition of a finite set’, Math. Proc. Cambridge Philos. Soc., to appear, arXiv:1404.1598.Google Scholar
Araújo, J. and Schneider, C., ‘The rank of the endomorphism monoid of a uniform partition’, Semigroup Forum 78(3) (2009), 498510.CrossRefGoogle Scholar
Dolinka, I. and East, J., ‘Idempotent generation in the endomorphism monoid of a uniform partition’, Comm. Algebra, to appear, arXiv:1407.3312V2.Google Scholar
Gomes, G. and Howie, J. M., ‘On the ranks of certain finite semigroups of transformations’, Math. Proc. Cambridge Philos. Soc. 101(3) (1987), 395403.CrossRefGoogle Scholar
Howie, J. M., ‘The subsemigroup generated by the idempotents of a full transformation semigroup’, J. Lond. Math. Soc. (2) 41 (1966), 707716.CrossRefGoogle Scholar
Howie, J. M., ‘Idempotent generators in finite full transformation semigroups’, Proc. Roy. Soc. Edinburgh Sect. A 81(3–4) (1978), 317323.CrossRefGoogle Scholar
Wright, E. M., ‘The number of irreducible tournaments’, Glasg. Math. J. 11 (1970), 97101.CrossRefGoogle Scholar
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