Idempotent rank in the endomorphism monoid of a non-uniform partition
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.
Citation
Dolinka , I , East , J & Mitchell , J D 2016 , ' Idempotent rank in the endomorphism monoid of a non-uniform partition ' , Bulletin of the Australian Mathematical Society , vol. 93 , no. 1 , pp. 73-91 . https://doi.org/10.1017/S0004972715000751
Publication
Bulletin of the Australian Mathematical Society
Status
Peer reviewed
ISSN
0004-9727Type
Journal article
Collections
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