翻訳と辞書 Words near each other ・ Finite element exterior calculus ・ Finite element limit analysis ・ Finite element machine ・ Finite element method ・ Finite element method in structural mechanics ・ Finite element model data post-processing ・ Finite element updating ・ Finite extensions of local fields ・ Finite field ・ Finite field arithmetic ・ Finite Fourier transform ・ Finite geometry ・ Finite group ・ Finite impulse response ・ Finite intersection property ・ Finite lattice representation problem ・ Finite Legendre transform ・ Finite map ・ Finite mathematics ・ Finite model property ・ Finite model theory ・ Finite morphism ・ Finite number ・ Finite part ・ Finite pointset method ・ Finite potential well ・ Finite Records ・ Finite ring ・ Finite Risk insurance ・ Finite set Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Finite lattice representation problem ： ウィキペディア英語版 Finite lattice representation problem In mathematics, the finite lattice representation problem, or finite congruence lattice problem, asks whether every finite lattice is isomorphic to the congruence lattice of some finite algebra. == Background == A lattice is called algebraic if it is complete and compactly generated. In 1963, Grätzer and Schmidt proved that every algebraic lattice is isomorphic to the congruence lattice of some algebra.〔G. Grätzer and E. T. Schmidt, ''Characterizations of congruence lattices of abstract algebras'', Acta Sci. Math. (Szeged) 24 (1963), 34–59.〕 Thus there is essentially no restriction on the shape of a congruence lattice of an algebra. The finite lattice representation problem asks whether the same is true for finite lattices and finite algebras. That is, does every finite lattice occur as the congruence lattice of a ''finite'' algebra? In 1980, Pálfy and Pudlák proved that this problem is equivalent to the problem of deciding whether every finite lattice occurs as an interval in the subgroup lattice of a finite group.〔Pálfy and Pudlák. ''Congruence lattices of finite algebras and intervals in subgroup lattices of finite groups.'' Algebra Universalis 11(1), 22–27 (1980). (DOI )〕 For an overview of the group theoretic approach to the problem, see Pálfy (1993)〔Péter Pál Pálfy. ''Intervals in subgroup lattices of finite groups.'' In Groups ’93 Galway/St. Andrews, Vol. 2, volume 212 of London Math. Soc. Lecture Note Ser., pages 482–494. Cambridge Univ. Press, Cambridge, 1995.〕 and Pálfy (2001).〔Péter Pál Pálfy. ''Groups and lattices.'' In Groups St. Andrews 2001 in Oxford. Vol. II, volume 305 of London Math. Soc. Lecture Note Ser., pages 428–454, Cambridge, 2003. Cambridge Univ. Press.〕 This problem should not be confused with the congruence lattice problem. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Finite lattice representation problem」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.