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Sur les treillis de Coxeter finis

C. Le Conte de Poly-Barbut (1994)

Mathématiques et Sciences Humaines

Björner (1984) a montré que l’ordre faible de Bruhat défini sur un groupe de Coxeter fini (Bourbaki 1969) est un treillis. Dans le cas du groupe symétrique S n ce résultat (treillis permutoèdre) a été prouvé par Guilbaud-Rosenstiehl (1963). Dans ce papier nous montrons que des propriétés connues des treillis permutoèdres peuvent s’étendre à tous les treillis de Coxeter finis et qu’inversement des propriétés démontrées sur tous les Coxeter finis ont des retombées intéressantes sur les permutoèdres....

SV and related f -rings and spaces

Suzanne Larson (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

An f -ring A is an SV f -ring if for every minimal prime ℓ -ideal P of A , A / P is a valuation domain. A topological space X is an SV space if C ( X ) is an SV f -ring. SV f -rings and spaces were introduced in [HW1], [HW2]. Since then a number of articles on SV f -rings and spaces and on related f -rings and spaces have appeared. This article surveys what is known about these f -rings and spaces and introduces a number of new results that help to clarify the relationship between SV f -rings and spaces and related...

The Bordalo order on a commutative ring

Melvin Henriksen, Frank A. Smith (1999)

Commentationes Mathematicae Universitatis Carolinae

If R is a commutative ring with identity and ≤ is defined by letting a ≤ b mean a b = a or a = b , then ( R , ≤ ) is a partially ordered ring. Necessary and sufficient conditions on R are given for ( R , ≤ ) to be a lattice, and conditions are given for it to be modular or distributive. The results are applied to the rings Z n of integers mod n for n ≥ 2 . In particular, if R is reduced, then ( R , ≤ ) is a lattice iff R is a weak Baer ring, and ( R , ≤ ) is a distributive lattice iff R is a Boolean ring, Z 3 , Z 4 , Z 2 [ x ] / x 2 Z 2 [ x ] , or a four element field.

Currently displaying 961 – 980 of 1272