Título inglés | Representation of algebraic distributive lattices with À_{1} compact elements as ideal lattices of regular rings. |
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Título español | Representación de retículos distributivos algebraicos con À_{1} 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 À_{1} compact elements is isomorphic to the ideal lattice of a von Neumann regular ring R.(By earlier results of the author, the À _{1} 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 |

Acceso al artículo completo |