Motivated by recent works on the genus of classifying spaces of compact Lie groups, here we study the set of filtered λ-ring structures over a filtered ring from a purely algebraic point of view. From a global perspective, we first show that this set has a canonical topology compatible with the filtration on the given filtered ring. For power series rings R[[x]], where R is between Z and Q, wit...

Motivated in part by recent works on the genus of classifying spaces of compact Lie groups, here we study the set of filtered λ-ring structures over a filtered ring from a purely algebraic point of view. From a global perspective, we first show that this set has a canonical topology compatible with the filtration on the given filtered ring. For power series rings R[[x]], where R is between Z an...

A ring $R$ is called a left Ikeda-Nakayama (left IN-ring) if the right annihilator of intersection any two ideals sum annihilators. As generalization IN-rings, SA-ring annihilators an ideal $R$. It natural to ask IN and SA property can be extended from $R[x; \alpha, \delta]$. In this note, results concerning conditions will allow these properties transfer skew polynomials $R[x;\alpha,\delta]$ a...

Five commercially available encryption packages for the IBM PC are described and broken.

In this paper we examine a certain filtration on topological Hochschild homology. This filtration has the virtue that it respects the cyclic structure of topological Hochschild homology, and therefore it is compatible with the cyclotomic structure used to define topological cyclic homology. As an example we show how the skeleton filtration of a simplicial ring gives rise to spectral sequences s...

For a field F of characteristic different from 2, containing a square root of -1, endowed with an F-compatible valuation v such that the residue field has at most two square classes, we use a combinatorial analogue of the Witt ring of F to prove that an anisotropic quadratic form over F with even dimension d, trivial discriminant and Hasse-Witt invariant can be written in the Witt ring as the s...

The paper discusses the development of an IBM PC based tool, for calculating train braking distances for various train classes on a rail network. There is discussion on current industry practice and the limitations of that practice, the concept of the tool itself, including the assumptions made, the strategy adopted to minimise the risk of incorrect calculations, and the results of adopting tha...

A further commercially available encryption package for the IBM PC is analysed, and a simple breaking program is described.

We prove a local monodromy theorem for p-adic differential equations on an annulus, answering a question of R. Crew. Specifically, suppose given a finite free module over the Robba ring (the ring of germs of functions analytic on some open p-adic annulus with outer radius 1) with a connection and a compatible Frobenius structure. We prove that the module admits a basis over a finite extension o...

By a topological ring we mean a ring X with a Hausdorff topology such that (x, y) 7→ x + y, x 7→ −x, (x, y) 7→ x · y are continuous. A morphism of topological rings is a continuous homomorphism of rings. An inverse system of topological rings is a family of topological rings Xi and a family of morphisms πi,j : Xi → Xj for i, j ∈ I with i ≥ j, such that when i ≥ j ≥ k, πi,k = πj,k ◦ πi,j . If Y ...