منابع مشابه
Congruence Lattices 101
This lecture—based on the author's book, General Lattice Theory , Birkhäuser Verlag, 1978—briefly introduces the basic concepts of lattice theory, as needed for the lecture " Some combinatorial aspects of congruence lattice representations ". 1.1. Posets. A partially ordered set A; ≤≤ consists of a nonvoid set A and a binary relation ≤ on A such that the relation ≤ satisfies properties (P1)–(P3...
متن کاملCongruence Lattices of Uniform Lattices
A lattice L is uniform, if for any congruence Θ of L, any two congruence classes A and B of Θ are of the same size, that is, |A| = |B| holds. A classical result of R. P. Dilworth represents a finite distributive lattice D as the congruence lattice of a finite lattice L. We show that this L can be constructed as a finite uniform lattice.
متن کاملDistributive Congruence Lattices of Congruence-permutable Algebras
We prove that every distributive algebraic lattice with at most א1 compact elements is isomorphic to the normal subgroup lattice of some group and to the submodule lattice of some right module. The א1 bound is optimal, as we find a distributive algebraic lattice D with א2 compact elements that is not isomorphic to the congruence lattice of any algebra with almost permutable congruences (hence n...
متن کاملCongruence Lattices of Congruence Semidistributive Algebras
Nearly twenty years ago, two of the authors wrote a paper on congruence lattices of semilattices [9]. The problem of finding a really useful characterization of congruence lattices of finite semilattices seemed too hard for us, so we went on to other things. Thus when Steve Seif asked one of us at the October 1990 meeting of the AMS in Amherst what we had learned in the meantime, the answer was...
متن کاملComputing Congruence Lattices 3
An inequality between the number of coverings in the ordered set J(Con L) of join irreducible congruences on a lattice L and the size of L is given. Using this inequality it is shown that this ordered set can be computed in time O(n 2 log 2 n), where n = jLj. This paper is motivated by the problem of eeciently calculating and representing the congruence lattice Con L of a nite lattice L. Of cou...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 1999
ISSN: 0304-3975
DOI: 10.1016/s0304-3975(98)00275-8