Idempotent rank in the endomorphism monoid of a non-uniform partition
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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.
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 . DOI: 10.1017/S0004972715000751
Bulletin of the Australian Mathematical Society
© 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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