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Hyperdecidability of pseudovarieties of orthogroups

Published online by Cambridge University Press:  04 June 2001

Jorge Almeida  and
Peter G. Trotter
Jorge Almeida
Affiliation:
Centro de Matemática da Universidade do Porto, P. Gomes Teixeira, 4099-002 Porto, Portugal e-mail:jalmeida@fc.up.pt
Peter G. Trotter
Affiliation:
Department of Mathematics, University of Tasmania, GPO Box 252-37 Hobart, Tasmania 7001, Australia e-mail:trotter@hilbert.maths.edu.au
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Let W denote the intersection with the pseudovariety of completely regular semigroups of the Mal'cev product of the pseudovariety of bands with a pseudovariety V of completely regular semigroups. It is shown that the (pseudo)word problem for W is reduced to that for V in such a way that decidability is preserved in the case in which terms involving only multiplication and weak inversion are considered. It is also shown that, if V is a hyperdecidable (respectively canonically reducible) pseudovariety of groups, then so is W.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 43 , Issue 1 , January 2001 , pp. 67 - 83
Copyright
2001 Glasgow Mathematical Journal Trust