منابع مشابه
About Free Lattices and Free Modular Lattices
Ralph Freese Department of Mathematics University of Hawaii at Manoa Honolulu, Hawaii 96822 In this paper we look at some of the problems on free lattices and free modular lattices which are of an order theoretic nature. We review some of the known results, give same new results, and present several open problems. Every countable partially ordered set can be order embedded into a countable free...
متن کاملFree μ - lattices ∗
A μ-lattice is a lattice with the property that every unary polynomial has both a least and a greatest fix-point. In this paper we define the quasivariety of μ-lattices and, for a given partially ordered set P , we construct a μ-lattice JP whose elements are equivalence classes of games in a preordered class J (P ). We prove that the μ-lattice JP is free over the ordered set P and that the orde...
متن کاملFree Groups in Lattices
Let G be any locally compact metrizable group. The main result of this paper, roughly stated, is that if F < G is any finitely generated free group and Γ < G any lattice, then up to a small perturbation and passing to a finite index subgroup, F is a subgroup of Γ. If G/Γ is noncompact then we require additional hypotheses that include G = SO(n, 1). MSC: 20E07, 20F65, 20F67, 22D40, 20E05.
متن کاملFree Lattices over Halflattices
0. INTRODUCTION. Although the word problem for free lattices is well known to be solvable (cf. Dean [1]), the question still remains open to characterize the finite partial lattices P for which the free lattice F (P ) over P is finite. There are partial answers to this question. In Wille [5] the problem is solved for the partial lattices P that are both meet– and join–trivial in the sense that ...
متن کاملPartition Representations of Free Lattices
I. Introduction. If 5 is a set, we will denote by G>(S) the lattice of all partitions (equivalence relations) of S. Whitman [6] proved that any lattice L is isomorphic to a sublattice of (P(S) for some 5. His proof shows that, if L is infinite, we can take 5 to be no larger than L; for finite L, however, his proof only shows that 5 can be taken count-able. This leaves open the following (still ...
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ژورنال
عنوان ژورنال: BRICS Report Series
سال: 2000
ISSN: 1601-5355,0909-0878
DOI: 10.7146/brics.v7i28.20161