Congruence Lattices of Finite Semimodular Lattices
نویسندگان
چکیده
منابع مشابه
Congruence Lattices of Finite Semimodular Lattices
We prove that every finite distributive lattice can be represented as the congruence lattice of a finite (planar) semimodular lattice.
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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(n2 log2 n), where n = |L|. This paper is motivated by the problem of efficiently calculating and representing the congruence lattice Con L of a finite lattice L. Of c...
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A semimodular lattice L of finite length will be called an almost-geometric lattice, if the order J(L) of its nonzero join-irreducible elements is a cardinal sum of at most two-element chains. We prove that each finite distributive lattice is isomorphic to the lattice of congruences of a finite almost-geometric lattice.
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In this paper we prove that if the congruence lattice of an automaton A is finite then the endomorphism semigroup E(A) of A is finite. Moreover, if A is commutative then A is A-finite. We prove that if 3 ≤ |A| then a commutative automaton A is simple if and only if it is a cyclic permutation automaton of prime order. We also give some results concerning cyclic, strongly connected and strongly t...
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ژورنال
عنوان ژورنال: Canadian Mathematical Bulletin
سال: 1998
ISSN: 0008-4395,1496-4287
DOI: 10.4153/cmb-1998-041-7