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The modularity of the lattice of varieties of completely regular semigroups and related representations
Published online by Cambridge University Press: 18 May 2009
Extract
A semigroup endowed with a unary operation satisfying the identities
is a completely regular semigroup. In several recent papers devoted to the study of the lattice of subvarieties of the variety
of completely regular semigroups, various results have been obtained which decompose special intervals in
into either direct products or subdirect products. Petrich [14], Hall and Jones [6] and Rasin [20] have shown that certain intervals of the form
, where
is the trivial variety and
are subdirect products of
and
Pastijn and Trotter [13] show that certain intervals of the form
are direct products of the intervals
and
The main objective of this paper is to develop an appropriate lattice theoretic framework for these representations.
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- Research Article
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- Copyright © Glasgow Mathematical Journal Trust 1990
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