Semigroups and their lattice of congruences

1983 ◽  
Vol 26 (1) ◽  
pp. 1-63 ◽  
Author(s):  
Heinz Mitsch
Keyword(s):  
Lattice Of Congruences

On Lattice-Ordered Rees Matrix Γ-Semigroups

2013 ◽  
Vol 59 (1) ◽  
pp. 209-218 ◽  
Author(s):  
Kostaq Hila ◽  
Edmond Pisha
Keyword(s):  
Structure Theorem ◽  
Lattice Of Congruences

Abstract The purpose of this paper is to introduce and give some properties of l-Rees matrix Γ-semigroups. Generalizing the results given by Guowei and Ping, concerning the congruences and lattice of congruences on regular Rees matrix Γ-semigroups, the structure theorem of l-congruences lattice of l - Γ-semigroup M = μº(G : I; L; Γe) is given, from which it follows that this l-congruences lattice is distributive.

XII.—The Lattice of Congruences on a Bisimple ω-Semigroup

1967 ◽  
Vol 67 (3) ◽  
pp. 175-184
Author(s):  
W. D. Munn
Keyword(s):  
Inverse Semigroup ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Natural Numbers ◽  
Necessary And Sufficient ◽  
Lattice Of Congruences

SynopsisA necessary and sufficient condition is determined for the modularity of the lattice of congruences on a bisimple inverse semigroup whose semilattice of idempotents is order-anti-isomorphic to the set of natural numbers.

scholarly journals Modularity of the lattice of congruences of a regular ω-semigroup

1990 ◽  
Vol 33 (3) ◽  
pp. 405-417 ◽  
Author(s):  
C. Bonzini ◽  
A. Cherubini
Keyword(s):  
Congruence Lattice ◽  
The One ◽  
Lattice Of Congruences

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.

scholarly journals Semimodularity and bisimple ω-semigroups

1970 ◽  
Vol 17 (1) ◽  
pp. 79-81 ◽  
Author(s):  
H. E. Scheiblich
Keyword(s):  
Simple Semigroup ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Primitive Idempotent ◽  
Necessary And Sufficient ◽  
Lattice Of Congruences

Let S be a completely 0-simple semigroup and let Λ(S) be the lattice of congruences on S. G. Lallement (2) has described necessary and sufficient conditions on S for Λ(S) to be modular, and has shown that Λ(S) is always semimodular . This result may be stated: If S is 0-bisimple and contains a primitive idempotent, then Λ(S) is semimodular.

scholarly journals Congruences contained in an equivalence on a semigroup

1980 ◽  
Vol 29 (2) ◽  
pp. 162-176 ◽  
Author(s):  
P. R. Jones
Keyword(s):  
Subdirect Product ◽  
Congruence Lattices ◽  
Lattice Of Congruences

AbstractThe main theorem of this paper shows that the lattice of congruences contained is some equivalence π on a semigroup S can be decomposed into a subdirect product of sublattices of the congruence lattices on the ‘prinipal π-facotrsρ of S—the semigroups formed by adjoining zeroes to the π-classes—whenever these are well-defined. The theorem is then applied to various equavalences and classes of semigroups to give some new results and alternative proofs of known ones.

On a common abstraction of de Morgan algebras and Stone algebras

1983 ◽  
Vol 94 (3-4) ◽  
pp. 301-308 ◽  
Author(s):  
T. S. Blyth ◽  
J. C. Varlet
Keyword(s):  
Distributive Lattice ◽  
Subdirectly Irreducible ◽  
Bounded Distributive Lattice ◽  
Subdirect Irreducibility ◽  
De Morgan Algebras ◽  
Simple Equations ◽  
Lattice Of Congruences

SynopsisWe consider a common abstraction of de Morgan algebras and Stone algebras which we call an MS-algebra. The variety of MS-algebras is easily described by adjoining only three simple equations to the axioms for a bounded distributive lattice. We first investigate the elementary properties of these algebras, then we characterise the least congruence which collapses all the elements of an ideal, and those ideals which are congruence kernels. We introduce a congruence which is similar to the Glivenko congruence in a p-algebra and show that the location of this congruence in the lattice of congruences is closely related to the subdirect irreducibility of the algebra. Finally, we give a complete description of the subdirectly irreducible MS-algebras.

scholarly journals A note on congruences on orthodox semigroups

1985 ◽  
Vol 26 (1) ◽  
pp. 25-30
Author(s):  
D. B. McAlister
Keyword(s):  
Inverse Semigroup ◽  
Orthodox Semigroup ◽  
Explicit Construction ◽  
Lattice Of Congruences ◽  
Orthodox Semigroups

C. Eberhart and W. Williams [3] showed that the least inverse semigroup congruence , on an orthodox semigroup S, plays a very important role in determining the structure of the lattice of congruences on S. In this note we show that their results can be applied to give an explicit construction for the idempotent separating congruences on S in terms of idempotent separating congruences on S/.

scholarly journals The lattice of congruences of locally cyclic semigroups

1966 ◽  
Vol 42 (7) ◽  
pp. 682-684 ◽  
Author(s):  
Takayuki Tamura ◽  
Wallace Etterbeek
Keyword(s):  
Lattice Of Congruences

scholarly journals On the lattice of congruences on an eventually regular semigroup

1985 ◽  
Vol 38 (2) ◽  
pp. 281-286 ◽  
Author(s):  
P. M. Edwards
Keyword(s):  
Regular Semigroup ◽  
Subject Classification ◽  
Maximum Element ◽  
M 10 ◽  
Natural Equivalence ◽  
20 M 10 ◽  
Complete Sublattice ◽  
Eventually Regular Semigroup ◽  
Lattice Of Congruences

AbstractA natural equivalence θ on the lattice of congruences λ(S) of a semigroup S is studied. For any eventually regular semigroup S, it is shown that θ is a congruence, each θ-class is a complete sublattice of λ(S) and the maximum element in each θ-class is determined. 1980 Mathematics subject classification (Amer. Math. Soc.): 20 M 10.

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