Representation of algebraic distributive lattices with À₁ compact elements as ideal lattices of regular rings.

Título inglés	Representation of algebraic distributive lattices with À1 compact elements as ideal lattices of regular rings.
Título español	Representación de retículos distributivos algebraicos con À1 elementos compactos como retículos de ideales de anillos regulares.
Autor/es	Wehrung, Friedrich
Organización	Dép. Math. Univ. Caen II, Caen, Francia
Revista	0214-1493
Publicación	2000, 44 (2): 419-435, 21 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	We prove the following result: Theorem. Every algebraic distributive lattice D with at most À1 compact elements is isomorphic to the ideal lattice of a von Neumann regular ring R. (By earlier results of the author, the À1 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.
Clasificación UNESCO	120108
Palabras clave español	Retículos ; Anillos reticulados ; Anillos regulares
Código MathReviews	MR1800815
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