The following changes should be made in the statement of Theorem 3.1 and its proof.

A set function is said to be λ-convex if whenever A and B are in Σ with A ∩ B = φ, then

Let R be a commutative ring and {σ1,…,σn} a set of commuting automorphisms of R. Let T = be the skew Laurent polynomial ring in n indeterminates over R and let be the Laurent polynomial ring in n central indeterminates over R. There is an isomorphism φ of right R-modules between T and S given by φ(θj) = xj. We will show that the map φ induces a bijection between the prime ideals of T and the Γ-prime ideals of S, where Γ is a certain set of endomorphisms of the ℤ-module S. We can study the structure of the lattice of Γ-prime ideals of the ring S by using commutative algebra, and this allows us to deduce results about the prime ideal structure of the ring T. As an example, if R is a Cohen-Macaulay ℂ-algebra and the action of the σj on R is locally finite-dimensional, we will show that the ring T is catenary.

The classical Dvoretzky-Rogers theorem states that if E is a normed space for which l1(E)=l1{E} (or equivalently , then E is finite dimensional (see [12] p. 67). This property still holds for any lp (l<p<∞) in place of l1 (see [7]p. 104 and [2] Corollary 5.5). Recently it has been shown that this result remains true when one replaces l1 by any non nuclear perfect sequence space having the normal topology (see [14]). In this context, De Grande-De Kimpe [4] gives an extension of the Devoretzky-Rogers theorem for perfect Banach sequence spaces.

We show that if X is a Banach space of infinite dimension and μh is a Hausdorff measure, where h is continuous, then there exists a measurable set K ⊂ X such that 0<μh(K)< + ∞. We also characterize the normed spaces in which the unit ball can be covered by a sequence of balls whose radii rn < 1 converge to zero as n → ∞.

Let N(λ) be a square matrix polynomial, and suppose det N is a polynomial of degree d. Subject to a certain non-singularity condition we construct a d by d Hermitian matrix whose signature determines the numbers of zeros of N inside and outside the unit circle. The result generalises a well known theorem of Schur and Cohn for scalar polynomials. The Hermitian “test matrix” is obtained as the inverse of the Gram matrix of a natural basis in a certain Krein space of rational vector functions associated with N. More complete results in a somewhat different formulation have been obtained by Lerer and Tismenetsky by other methods.

In a previous paper we discussed the duals of generic hypersurfaces: both smooth hypersurfaces in ℝn and algebraic hypersurfaces in real or complex projective space ℙn. In this note we show how to extend the methods of [1] to cover the case of complete intersections in ℙn and preface this with a brief discussion on the contact of space curves in ℝn with planes. We shall use the notation of [1].

A necessary and sufficient condition for confluence of two poles of a class of meromorphic solutions of the KdV equation is introduced and proved.

In this paper we generalize the folding process initiated by Stallings for graphs to a class of generalized covering spaces. These spaces are called pinched coverings or pinched cores, depending on the particular situation. We then apply our generalized folding process to manipulate these spaces into actual coverings. By using elementary homotopy arguments, we can calculate the fundamental groups of these spaces. As a corollary to our main result we obtain a generalization of a result due to Gersten concerning monomorphisms between free products of groups.