Certain congruence and quotient lattices related to completely 0-simple and primitive regular semigroups
1969 ◽
Vol 10
(1)
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pp. 21-24
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Keyword(s):
G. Lallement [4] has shown that the lattice of congruences, Λ(S), on a completely 0-simple semigroupSis semimodular, thus improving G. B. Preston's result [5] that such a lattice satisfies the Jordan-Dedekind chain condition. More recently, J. M. Howie [2] has given a new and more simple proof of Lallement's result using work due to Tamura [9]. The purpose of this note is to extend the semimodularity result to primitive regular semigroups, to establish a theorem relating certain congruence and quotient lattices, and to provide a theorem for congruences on any regular semigroup.
1988 ◽
Vol 45
(3)
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pp. 320-325
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1971 ◽
Vol 12
(4)
◽
pp. 456-460
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Keyword(s):
1991 ◽
Vol 34
(2)
◽
pp. 179-203
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1969 ◽
Vol 1
(2)
◽
pp. 231-235
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1993 ◽
Vol 113
(3)
◽
pp. 519-533
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Keyword(s):
1980 ◽
Vol 29
(4)
◽
pp. 475-503
◽
1970 ◽
Vol 17
(1)
◽
pp. 79-81
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1996 ◽
Vol 39
(3)
◽
pp. 425-460
◽
1997 ◽
Vol 40
(3)
◽
pp. 457-472
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