群在分配格上的作用

Groups Acting on Distributive Lattices

本文将分配格的自同构群对分配格的作用推广成抽象的群对分配格的作用(即G-分配格),建立了G-有界分配格范畴和G-Priestley空间范畴的对偶等价性,并在此基础上刻画了G-同余关系的对偶以及G-分配格的次直不可约性和同余可换性。所得结论丰富了分配格、格群等代数理论。

In this paper we generalize its automorphism group acting on a distributive lattice to an abstract group, and give a dual equivalence between the category of G-distributive lattices and the category of G-Priestly spaces; we characterize subdireetly irreducible G-distributive lattices and con- gruence permutable G-distributive lattices. Results obtained enrich the theory of distributive lattices and lattice-groups.