On the congruence lattice of a Scott-domain

1993 ◽  
Vol 30 (2) ◽  
pp. 297-299 ◽  
Author(s):  
G. Gr�tzer ◽  
E. T. Schmidt

1983 ◽  
Vol 44 (3) ◽  
pp. 299-308 ◽  
Author(s):  
M.G. Stone ◽  
R.H. Weedmark


1998 ◽  
Vol 41 (3) ◽  
pp. 290-297 ◽  
Author(s):  
G. Grätzer ◽  
H. Lakser ◽  
E. T. Schmidt

AbstractWe prove that every finite distributive lattice can be represented as the congruence lattice of a finite (planar) semimodular lattice.



1993 ◽  
Vol 35 (1) ◽  
pp. 39-50 ◽  
Author(s):  
Mario Petrich

Let S be an ideal of a semigroup V. In such a case, V is an (ideal) extension of S by T = V/S. The problem considered in [2] is the construction of all congruences on V in terms of congruences on S and T. This did not succeed for all congruences but it did for those congruences whose restriction to S is weakly reductive. If the extension is strict, more precise constructions are also given there. With some relatively weak restrictions on S, we are able to obtain in this way all congruences on V in the form indicated above.



1990 ◽  
Vol 33 (3) ◽  
pp. 405-417 ◽  
Author(s):  
C. Bonzini ◽  
A. Cherubini

In this paper a characterization of the regular ω-semigroups whose congruence lattice is modular is given. The characterization obtained for such semigroups generalizes the one given by Munn for bisimple ω-semigroups and completes a result of Baird dealing with the modularity of the sublattice of the congruence lattice of a simple regular ω-semigroup consisting of congruences which are either idempotent separating or group congruences.



1972 ◽  
Vol 2 (1) ◽  
pp. 18-19 ◽  
Author(s):  
J. Berman
Keyword(s):  




1997 ◽  
Vol 40 (3) ◽  
pp. 457-472 ◽  
Author(s):  
Mario Petrich

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.





Sign in / Sign up

Export Citation Format

Share Document