Open Access
2012 On the Power Pseudovariety $\mathbf{PCS}$
K. Auinger
Publ. Mat. 56(2): 467-471 (2012).


The pseudovariety $\mathbf{PCS}$ which is generated by all power semigroups of finite completely simple semigroups is characterized in various ways. For example, the equalities

$$\mathbf{PCS}=\mathbf{J}\malcab \mathbf{CS} =\mathbf{BG}\malcab \mathbf{RB}$$

are established. This resolves a problem raised by Kaďourek and leads to several transparent algorithms for deciding membership in $\mathbf{PCS}$.


Download Citation

K. Auinger. "On the Power Pseudovariety $\mathbf{PCS}$." Publ. Mat. 56 (2) 467 - 471, 2012.


Published: 2012
First available in Project Euclid: 19 June 2012

zbMATH: 1306.20058
MathSciNet: MR2978331

Primary: 20M07 , 20M20 , 20M30

Keywords: completely simple semigroup , membership problem , power operator , power pseudovariety , Power semigroup

Rights: Copyright © 2012 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.56 • No. 2 • 2012
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