Two congruence lattices of completely simple semigroups |
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Authors: | Mario Petrich |
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Institution: | (1) Dipartimento di Matematica, Università di Lecce, I-73 100 Lecce, Italia |
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Abstract: | For a Rees matrix semigroupS with normalized sandwich matrix and C(S), the congruence lattice ofS, we consider the lattice generated by {itpTl, pK, pTr, ptl, pk, ptr}. HerepT
1 andpt
l
are the upper and lower ends of the interval which makes up the
i
-class of ,
i
being the left trace relation onC(S). The remaining symbols have the analogous meaning relative to the kernel and the right trace relations. We also consider the lattice generated by {T
l, K, Tr, tl, k, tr} where and are the equality and the universal relations onS, respectively. In both cases, we find lattices freest relative to these lattices and represent them as distributive lattices with generators and relations.With 3 Figures |
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Keywords: | |
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