Strong rightD-domains

An integral domainR is called rightD-domain if its lattice of all right ideals is distributive. In § 2 a sufficient condition for an integral domainR is given such thatR is a rightD-domain if and only ifR is a leftD-domain. For example each integral domain which is algebraic over its center satisfies this criterion. Furthermore, a rightD-domain is called strong if its lattice of all fractional right ideals is distributive. Examples of strong rightD-domains are given in §4. Each overring of a strong rightD-domain is also a strong rightD-domain whereas arbitrary rightD-domains may have overrings which are no rightD-domains. Section 3 is mainly concerned with the set * of all left invertible fractional right ideals and the mapping :**,II _l ^–1 whereI _l ^–1 denotes the left inverse ofI. For example, equivalent conditions are given for * to be a sublattice of and it is shown that is bijective if and only if (IJ)=(I)+(J) holds for allI,J*. Finally, §5 deals with (right)D-domains which are algebraic over their centersC. It is proved thatR is invariant if and only ifC is a commutative Prüfer domain andR the integral closure ofC inQ(R).     

Study of a filtration expanded to include an honest time

Summary Let (,, P) be a measurable space, and { _t} be a filtration on (,). Then, given a fixed honest timeL a new filtrationG _t} is defined, the smallest containing { _t} and for whichL is a stopping time, and the martingales, semimartingales and stopping times of this new filtration are characterised.     

On the homogeneous Riemannian structures of type ℐ1⊕ℐ3

We study homogeneous Riemannian structures belonging to the class ₁₃ of the classification given by Tricerri and Vanhecke. The main result is the following: a connected, simply connected Riemannian manifoldM admits a homogeneous structureT of type ₁₃,T₃, if and only ifM is isometric to a hyperbolic space ⁿ .This work was partially supported by M.P.I.     

Singular points of a star-finite tiling

Let be a star-finite tiling of a topological vector space of dimension greater than one and let S() denote the set of singular points of . We show that S() is either uncountable or empty by investigating the density in S() of certain subcollections of geometrically interesting singular points.     

Complements to ‘The Bruhat order on symmetric varieties’

We give several complements to the paper The Bruhat order on symmetric varieties. Our main result shows that the partial order on the set of twisted involutions in the Weyl groupW, which was introduced in the earlier paper, agrees with the partial order on induced by the usual Bruhat order onW.R. W. Richardson died on 15 June. 1993.     

Hyperaffine planes over hyperfields

Summary In this paper we solve the problem of finding suitable conditions for an hyperaffine plane (,) under which a planar hyperfield K exists such that (,) is isomorphic to the hyperaffine plane (K²,').Research partially supported by C.N.R.-G.N.S.A.G.A.     

Présentations des groupes de Fischer (II)

In this paper we give Coxeter presentation (X, ) for the three Fischer groupsG=Fi₂₂, Fi₂₃, Fi₂₄; we apply methods exposed in the first part. Each of these groups is generated by a class of 3-transpositions (named here a Fischer class) in which elements ofX are chosen. A subset of is the set of all the relations (xy) ^m(x,y)=1, wherex andy are inX and wherem(x,y) means the order ofxy inG. We obtainG as a specified quotient of the Coxeter group (X, ) with the appropriate diagram .     

Groups acting simply transitively on the vertices of a building of typeà 2, II: The casesq=2 andq=3

If (P, L) is a projective plane and is a triangle presentation compatible with a point-line correspondence :P L, then gives rise to a group and a thick building of typeà ₂ on the vertices of which acts simply transitively. We find all triangle presentations (up to natural equivalence) compatible with some point-line correspondence :P L, when (P, L) is the projective plane of orderq=2 orq=3. For some, but not all, of these , is isomorphic to the building associated withG=PGL(3,K) whereK is a local field with discrete valuation and residual field of orderq. We identify the for which this is the case, and in these cases, find embeddings of intoG. We also describe the arithmetic nature of these groups.     

Tessellations generated by hyperplanes

Let be a locally finite system of hyperplanes in ^d with the property that the cells of the induced cell complex decomposition of ^d have uniformly bounded diameters. If is simple and the density of the vertices in exists, then the density of thek-cells in exists and can be given explicitly (k = 1, ...,d). Also, the mean number ofj-faces of thek-cells in exists and can be calculated. For certain nonsimple systems , corresponding inequalities are obtained.     

On the divisibility of homogeneous hypergraphs

We denote byK _k ,k, 2, the set of allk-uniform hypergraphsK which have the property that every element subset of the base ofK is a subset of one of the hyperedges ofK. So, the only element inK ₂ ² are the complete graphs. If is a subset ofK _k then there is exactly one homogeneous hypergraphH whose age is the set of all finite hypergraphs which do not embed any element of . We callH -free homogeneous graphsH _n have been shown to be indivisible, that is, for any partition ofH _n into two classes, oue of the classes embeds an isomorphic copy ofH _n . [5]. Here we will investigate this question of indivisibility in the more general context of-free homogeneous hypergraphs. We will derive a general necessary condition for a homogeneous structure to be indivisible and prove that all-free hypergraphs for K _k with 3 are indivisible. The-free hypergraphs with K _k ² satisfy a weaker form of indivisibility which was first shown by Henson [2] to hold forH _n . The general necessary condition for homogeneous structures to be indivisible will then be used to show that not all-free homogeneous hypergraphs are indivisible.This research has been supported by NSERC grant 69–1325.     

Présentations des groupes de Fischer (I)

This work gives a method for constructing presentation (X, ) for a group generated by a class of 3-transpositions (named here a Fischer class) in which {ie275-1}(G/Z(G)) is simple and non-abelian. The generating set X is contained in D; is the set of relations (xy) ^m(x,y)=1, x and y in X, where m(x, y) is the order of the product xy in G, m(x, y) 3; is a set of relations between elements of X. The group G is constructed as a quotient of the Coxeter group (X, ).These results are applied to symplectic and orthogonal groups over {ie275-2}. Applications to other groups, in particular to the sporadic Fischer groups, will follow later.     

On the geometric structure of independence systems

A bouquet of matroids is a combinatorial structure that generalizes the properties of matroids. Given an independence system, there exist several bouquets of matroids having the same family of independent sets. We show that the collection of these geometries forms in general a meet semi-lattice and, in some cases, a lattice (for instance, when is the family of the stable sets in a graph). Moreover, one of the bouquets that correspond to the highest elements in the meet semi-lattice provides the smallest decomposition of into matroidal families, such that the rank functions of the different matroids have the same values for common sets. In the last section, we give sharp bounds on the performance of the greedy algorithm, using parameters of some special bouquets in the semi-lattice.     

Identical relations for the forms with a Young symmetry

Let there be given a Young symmetrizere . Consider the space of multilinear forms obtained by actione . In the paper the characteristic property in terms of identities is found for a multilinear form to belong to this space. This property is analogous to the well-known identities for the cases of the spaces of the symmetric and skew-symmetric forms. In addition, a generalization of Garnir identities is obtained.     

First order properties of random posets

Let =(n,p) be a binary relation on the set [n]={1, 2, ..., n} such that (i,i) for every i and (i,j) with probability p, independently for each pair i,j [n], where i<j. Define as the transitive closure of and denote poset ([n], ) by R(n, p). We show that for any constant p probability of each first order property of R(n, p) converges as n .     

Some properties of lattices of radical classes of lattice-ordered groups

Aradical class of lattice-ordered groups (-groups) is a class closed under taking convex-subgroups, joins of convex-subgroups, and-isomorphic images. Imposing various other closure conditions leads to many specific types of radical classes (e.g., torsion classes). For several of these types, the complete latticeT of radical classes of that type has been studied, and such latticesT are our object of study here. We give the characteristic properties of closed-kernel radical mappings and polar kernel radical mappings. We prove in many instances thatT isrelatively polarized, that is, for any ], T with ] there exists a unique largest T such that = ], and often we are able to explicitly identify. By using these properties we characterize meet irreducibility in the latticeT of polar kernel radical classes.Presented by M. Henriksen.     

Realizations of regular polytopes

Let be a finite regular incidence-polytope. A realization of is given by an imageV of its vertices under a mapping into some euclidean space, which is such that every element of the automorphism group () of induces an isometry ofV. It is shown in this paper that the family of all possible realizations (up to congruence) of forms, in a natural way, a closed convex cone, which is also denoted by The dimensionr of is the number of equivalence classes under () of diagonals of , and is also the number of unions of double cosets ^{** *–1*} ( ^*), where ^* is the subgroup of () which fixes some given vertex of . The fine structure of corresponds to the irreducible orthogonal representations of (). IfG is such a representation, let its degree bed _G , and let the subgroup ofG corresponding to ^* have a fixed space of dimensionw _G . Then the relations

Homotopy types for tamely approximable Sobolev maps between manifolds

We define a class ^p (M,N) of Sobolev maps from a manifoldM into a manifoldN, in such a way that each mapu ^p (M, N) has a well defined [p]-homotopy type, providedN satisfies a topological hypothesis. Using this, we prove the existence of minimizers in [p]-homotopy classes for some polyconvex variational problems.     

Arithmetic and other properties of certain Delphic semigroups. I

Summary Some aspects of Delphic semigroups in general — in particular, the idea of an hereditary subsemigroup, which has many uses in connexion with Delphic semigroups — are first treated. After that, attention is directed to the arithmetic of ⁺, the semigroup of positive renewal sequences. In a Delphic semigroup the aboriginal elements are the simples and the members of I ₀: a class of simples of ⁺ is constructed and the simples are shown to be residual. I ₀ is explicitly identified, and this leads to a canonical factorization of ⁺. The properties of division in ⁺ are discussed.     

A gaussian central limit theorem for trimmed products on simply connected step 2-Nilpotent Lie groups

A limit theorem due to J. Kuelbs and M. Ledoux, valid for dilatation-stable laws on type 2-Banach spaces, is carried over to stable laws on simply connected step 2-nilpotent Lie groupsG. We show that for products of i.i.d. random variables in the of attraction of a nondegenerate semigroup onG, where is a one-parameter automorphism group acting contracting onG, a certain intermediate trimming procedure, together with a suitable norming, always yields a nondegenerate centered Gaussian limit.     

On Random Sets Connected to the Partial Records of Poisson Point Process

Random intervals are constructed from partial records in a Poisson point process in ]0,[×]0,[. These are used to cover partially [0,[; the purpose of this work is to study the random set that is left uncovered. We show that enjoys the regenerative property and identify its distribution in terms of the characteristics of the Poisson point process. As an application we show that is almost surely a fractal set and we calculate its dimension.