We show that several "good" properties of the standard part map on regular Hausdorff spaces do not hold for arbitrary Hausdorff spaces.

The relations between the adjoint group and the additive group of a radical ring and its nilpotency are investigated. It is shown that certain finiteness conditions carry over from the adjoint group to the additive group and that the converse holds for the class of minimax groups.

Let γ(t) = (t, t2,..., tn) + a be a curve in Rn, where n ≥ 2 and a ∊ Rn. We prove LP-Lq estimates for the weighted lacunary maximal function, related to this curve, defined by

If n = 2 or 3 our results are (nearly) sharp.

An F-measure on a Cartesian product of algebras of sets is a scalar-valued function which is a scalar measure independently in each coordinate. It is demonstrated that an F-measure on a product of algebras determines an F-measure on the product of the corresponding σ-algebras if and only if its Fréchet variation is finite. An analogous statement is obtained in a framework of fractional Cartesian products of algebras, and a measurement of p-variation of F-measures, based on Littlewood-type inequalities, is discussed.

Si (A0,A1) est un couple d'interpolation et si A0 est uniformément convexe on montre que pour tous θ1, θ2 ∊ ]0,1 [ il existe un homéomorphisme uniforme entre la sphère unité de (A0,A1)θ1 et la sphère unité de (A0, A1)θ2.

We consider operators T of the form Tf = {Tjfj}, where Tjfj(x) = (p. v) ∫Rn kj(x — y)fj(y) dy. Under appropriate conditions on the kj, two-weighted estimates for T are obtained, the weights being radial and suitably linked.

Nous proposons de construire des polynômes à coefficients p-adiques, de degré D, sans terme constant, ayant plus que 2D + 1 variables. Ces polynômes n'ont dans Zp que le zéro trivial modulo p2. Le but que nous cherchons à atteindre, à partir des polynômes ainsi construit, est de minorer les valeurs de p pour lesquelles l'équation F(x1,...,X2D+1) ≡ 0 (mod p2) admet une solution primitive, F est un élément de Zp[X1,... ,X2D+1] de degré D sans term constant.

We give a characterisation of where and are subspace lattices with commutative and either completely distributive or complemented. We use it to show that Lat is a CSL algebra with a completely distributive or complemented lattice and is any operator algebra.

Special cases of Bovdi's conjecture are proved. In particular the conjecture is proved for supersolvable and Frobenius groups. We also prove that if is finite, α ∊ VℤG a torsion unit and m the smallest positive integer such that αm ∊ G then m divides .

In this paper, we show that the lattice of closed subsets of the completion, in the Jacobson radical topology, of a finitely generated module M is isomorphic to the completion, under the Hausdorff topology, of the lattice of closed subsets of M. This extends submodule-theoretic results for complete modules to modules satisfying Chevalley's Theorem. We show that the lattice of submodules of every finitely generated module over a semi-local ring R is complete in the Hausdorff topology if and only if R is complete in the Jacobson radical topology.

Results are given for a class of square {0,1}-matrices which provide information about the 4-rank of the ideal class group of certain quadratic number fields.

We prove that given an operator space structure on a dual Banach space Y*, it is not necessarily the dual one of some operator space structure on Y. This allows us to show that Sakai's theorem providing the identification between C*-algebras having a predual and von Neumann algebras does not extend to the category of operator spaces. We also include a related result about completely bounded operators from B(ℓ2)* into the operator Hilbert space OH.

By using the principle of mathematical induction a simple algebraic formula is derived for an m-dimensional Schlömilch series. The result yields a countably infinite number of representations for null-functions on increasingly larger open intervals.

Let be a Lie algebra homomorphism from the Lie algebra of G to the Lie algebra of H in the following cases: (i) G and H are irreducible algebraic groups over an algebraically closed field of characteristic 0, or (ii) G and H are linear complex analytic groups. In this paper, we present some equivalent conditions for ϕ to be a differential in the above two cases. That is, ϕ is the differential of a morphism of algebraic groups or analytic groups as appropriate.

In the algebraic case, for example, it is shown that ϕ is a differential if and only if ϕ preserves nilpotency, semisimplicity, and integrality of elements. In the analytic case, ϕ is a differential if and only if ϕ maps every integral semisimple element of into an integral semisimple element of , where G0 and H0 are the universal algebraic subgroups of G and H. Via rational elements, we also present some equivalent conditions for ϕ to be a differential up to coverings of G in the algebraic case, and for ϕ to be a differential up to finite coverings of G in the analytic case.

For finite-dimensional subspaces of ℓ∞ over a non-archimedean valued base field K we study orthocomplementation as related to the Hahn-Banach property and strictness. As a corollary we obtain that, if K is not spherically complete, a closed hyperplane in c0 having the Hahn-Banach property is orthocomplemented (Theorem 2.1, Remark 2).

In the paper we identify up to bordism all manifolds with (Z2)k-action whose fixed point set is Sn × Sm U point.

A series of elements of order 4 in the symplectic cobordism ring is constructed.

In this note, we show that a ring R is a left perfect ring if and only if every generating set of each left R-module contains a minimal generating set. This result gives a positive answer to a question on left perfect rings raised by Nashier and Nichols.