Per citar aquest document: http://ddd.uab.cat/record/1937
Representation of algebraic distributive lattices with N1 compact elements as ideal lattices of regular rings
Wehrung, Friedrich

Data: 2000
Resum: We prove the following result: Theorem. Every algebraic distributive lattice D with at most N1 compact elements is isomorphic to the ideal lattice of a von Neumann regular ring R. (By earlier results of the author, the N1 bound is optimal. ) Therefore, D is also isomorphic to the congruence lattice of a sectionally complemented modular lattice L, namely, the principal right ideal lattice of R. Furthermore, if the largest element of D is compact, then one can assume that R is unital, respectively, that L has a largest element. This extends several known results of G. M. Bergman, A. P. Huhn, J. Tuma, and of a joint work of G. Grätzer, H. Lakser, and the author, and it solves Problem 2 of the survey paper [10]. The main tool used in the proof of our result is an amalgamation theorem for semilattices and algebras (over a given division ring), a variant of previously known amalgamation theorems for semilattices and lattices, due to J. Tuma, and G. Grätzer, H. Lakser, and the author.
Drets: Tots els drets reservats.
Llengua: Anglès.
Document: Article ; recerca ; article ; publishedVersion
Publicat a: Publicacions matematiques, V. 44 N. 2 (2000) , p. 419-435, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_44200_03


17 p, 186.4 KB

El registre apareix a les col·leccions:
Articles > Articles publicats > Publicacions matemàtiques
Articles > Articles de recerca

 Registre creat el 2006-03-13, darrera modificació el 2016-06-12



   Favorit i Compartir