Canonical Varieties of Completely Regular Semigroups
2007 ◽
Vol 83
(1)
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pp. 87-104
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Keyword(s):
AbstractCompletely 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, VB] for V ∈ L(CR). Here VB = V ∩ B. We characterize VB in several ways, the principal one being an inductive way of constructing bases for v-irreducible band varieties. We term the latter canonical. We perform a similar analysis for the intersection of these varieties with the varieties BG, OBG and B.
1990 ◽
Vol 32
(2)
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pp. 137-152
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1983 ◽
Vol 35
(2)
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pp. 227-235
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1990 ◽
Vol 49
(1)
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pp. 1-23
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Keyword(s):
2013 ◽
Vol 42
(4)
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pp. 1397-1413
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2016 ◽
Vol 45
(7)
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pp. 2783-2794
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2018 ◽
Vol 55
(1)
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pp. 1-22
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2015 ◽
Vol 43
(10)
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pp. 4080-4096
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