On period maps that are open embeddings

MULTIPLICATION MODULES THAT ARE FINITELY GENERATED

Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. An $R$-module $M$ is called a multiplication module if for every submodule $N$ of $M$ there exists an ideal $I$ of $R$ such that $N = IM$. It is shown that over a Noetherian domain $R$ with dim$(R)leq 1$, multiplication modules are precisely cyclic or isomorphic to an invertible ideal of $R$. Moreover, we give a charac...

Maps that are roots of power series

We introduce a class of polynomial maps that we call polynomial roots of powerseries, and show that automorphisms with this property generate the automorphism group in any dimension. In particular we determine generically which polynomial maps that preserve the origin are roots of powerseries. We study the one-dimensional case in greater depth.

Embeddings of rearrangement invariant spaces that are not strictly singular

We give partial answers to the following conjecture: the natural embedding of a rearrangement invariant space E into L1([0, 1]) is strictly singular if and only if G does not embed into E continuously, where G is the closure of the simple functions in the Orlicz space LΦ with Φ(x) = exp(x 2) − 1. In this paper we ask the following question. Given a rearrangement invariant space E on [0, 1], whe...

Embeddings of Rearrangement Invariant Spaces That Are Not Strictly Singular

We give partial answers to the following conjecture: the natural embedding of a rearrangement invariant space E into L1 ((0; 1]) is strictly singular if and only if G does not embed into E continuously, where G is the closure of the simple functions in the Orlicz space L with (x) = exp(x 2) ? 1. In this paper we ask the following question. Given a rearrangement invariant space E on 0; 1], when ...

On open extensions of maps