Idempotent rank in the endomorphism monoid of a nonuniform partition

Igor Dolinka; James East; James D. Mitchell

doi:10.1017/S0004972715000751

Idempotent rank in the endomorphism monoid of a nonuniform partition

Igor Dolinka, James East, James D. Mitchell

School of Computer, Data & Mathematical Sciences

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

11 Citations (Scopus)

Abstract

We calculate the rank and idempotent rank of the semigroup Æ(X,P) generated by the idempotents of the semigroup T(X,P) which consists of all transformations of the finite set X preserving a nonuniform partition 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.

Original language	English
Pages (from-to)	73-91
Number of pages	19
Journal	Bulletin of the Australian Mathematical Society
Volume	93
Issue number	1
DOIs	https://doi.org/10.1017/S0004972715000751
Publication status	Published - 2016

Keywords

endomorphisms (group theory)
idempotents
monoids
semigroups of endomorphisms

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Cite this

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abstract = "We calculate the rank and idempotent rank of the semigroup {\AE}(X,P) generated by the idempotents of the semigroup T(X,P) which consists of all transformations of the finite set X preserving a nonuniform partition 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.",

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AB - We calculate the rank and idempotent rank of the semigroup Æ(X,P) generated by the idempotents of the semigroup T(X,P) which consists of all transformations of the finite set X preserving a nonuniform partition 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.

KW - endomorphisms (group theory)

KW - idempotents

KW - monoids

KW - semigroups of endomorphisms

UR - http://handle.uws.edu.au:8081/1959.7/uws:31452

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DO - 10.1017/S0004972715000751

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VL - 93

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EP - 91

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

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ER -

Idempotent rank in the endomorphism monoid of a nonuniform partition

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