A special sublattice of the congruence lattice of a regular semigroup
1997 ◽
Vol 40
(3)
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pp. 457-472
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Keyword(s):
Let S be a regular semigroup and be its congruence lattice. For ρ ∈ , we consider the sublattice Lρ of generated by the congruences pw where w ∈ {K, k, T, t}* and w has no subword of the form KT, TK, kt, tk. Here K, k, T, t are the operators on induced by the kernel and the trace relations on . We find explicitly the least lattice L whose homomorphic image is Lρ for all ρ ∈ and represent it as a distributive lattice in terms of generators and relations. We also consider special cases: bands of groups, E-unitary regular semigroups, completely simple semigroups, rectangular groups as well as varieties of completely regular semigroups.
1973 ◽
Vol 14
(1)
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pp. 27-49
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2013 ◽
Vol 94
(3)
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pp. 397-416
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1985 ◽
Vol 38
(3)
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pp. 372-393
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2019 ◽
Vol 29
(08)
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pp. 1383-1407
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1994 ◽
Vol 56
(2)
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pp. 212-231
2014 ◽
Vol 24
(05)
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pp. 531-551
1996 ◽
Vol 06
(06)
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pp. 655-685
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1991 ◽
Vol 34
(2)
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pp. 179-203
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