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

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

11 Citations (Scopus)

Abstract

We calculate the rank and idempotent rank of the semigroup Ɛ(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

Access to Document

10.1017/S0004972715000751

http://ezproxy.uws.edu.au/login?url=http://doi.org/10.1017/S0004972715000751

Cite this

@article{099d23fef2f14f9cb634ca53c86d6fb4,

title = "Idempotent rank in the endomorphism monoid of a nonuniform partition",

abstract = "We calculate the rank and idempotent rank of the semigroup Ɛ(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.",

keywords = "endomorphisms (group theory), idempotents, monoids, semigroups of endomorphisms",

author = "Igor Dolinka and James East and Mitchell, {James D.}",

year = "2016",

doi = "10.1017/S0004972715000751",

language = "English",

volume = "93",

pages = "73--91",

journal = "Bulletin of the Australian Mathematical Society",

issn = "1755-1633",

publisher = "Cambridge University Press",

number = "1",

}

TY - JOUR

T1 - Idempotent rank in the endomorphism monoid of a nonuniform partition

AU - Dolinka, Igor

AU - East, James

AU - Mitchell, James D.

PY - 2016

Y1 - 2016

N2 - We calculate the rank and idempotent rank of the semigroup Ɛ(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.

AB - We calculate the rank and idempotent rank of the semigroup Ɛ(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

U2 - 10.1017/S0004972715000751

DO - 10.1017/S0004972715000751

M3 - Article

SN - 1755-1633

SN - 0004-9727

VL - 93

SP - 73

EP - 91

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

IS - 1

ER -

Idempotent rank in the endomorphism monoid of a nonuniform partition

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this