Idempotent rank in the endomorphism monoid of a non-uniform partition

Igor Dolinka; James East; James D. Mitchell

doi:10.1017/S0004972715000751

Idempotent rank in the endomorphism monoid of a non-uniform partition

Igor Dolinka, James East, James D. Mitchell

Research output: Contribution to journal › Article › peer-review

Abstract

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

Original language	English
Pages (from-to)	73-91
Journal	Bulletin of the Australian Mathematical Society
Volume	93
Issue number	1
Early online date	10 Aug 2015
DOIs	https://doi.org/10.1017/S0004972715000751
Publication status	Published - Feb 2016

Keywords

Transformation semigroups
Idempotents
Generators
Rank
Idempotent rank

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10.1017/S0004972715000751

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© 2016, Publisher / the Author(s). This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at journals.cambridge.org / https://dx.doi.org/10.1017/S0004972715000751
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Cite this

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Idempotent rank in the endomorphism monoid of a non-uniform partition

Abstract

Keywords

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