The lattice of completely regular semigroup varieties
نویسندگان
چکیده
منابع مشابه
Two Operators on the Lattice of Completely Regular Semigroup Varieties
In this paper, varieties of completely regular semigroups are studied. This paper is divided into six sections. Section 1 contains an introduction to varieties of completely regular semigroups and preliminaries. Most of the notation needed in this paper is given. In Section 2, the operators ←− ( ) and −→ ( ) on the lattice of subvarieties of varieties of completely regular semigroups are invest...
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Completely regular semigroups CR are regarded here as algebras with multiplication and the unary operation of inversion. Their lattice of varieties is denoted by L.CR/. Let B denote the variety of bands and L.B/ the lattice of its subvarieties. The mapping V → V ∩ B is a complete homomorphism of L.CR/ onto L.B/. The congruence induced by it has classes that are intervals, say VB = [VB ;V B] for...
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Let S be a regular semigroup and C its lattice of congruences. We consider the sublattice Λ of C generated by σ-the least group, τ -the greatest idempotent pure, μ-the greatest idempotent separating and β-the least band congruence on S. To this end, we study the following special cases: (1) any three of these congruences generate a distributive lattice, (2) Λ is distributive, (3) the restrictio...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
سال: 1990
ISSN: 0263-6115
DOI: 10.1017/s1446788700030214