A Noether Skolem theorem for group-graded rings

Group - Graded Rings and Duality

We give an alternative construction of the duality between finite group actions and group gradings on rings which was shown by Cohen and Montgomery in [1]. This duality is then used to extend known results on skew group rings to corresponding results for large classes of group-graded rings. Finally we modify the construction slightly to handle infinite groups. Introduction. In the first section...

The Noether-lefschetz Theorem for the Divisor Class Group

Let X be a normal projective threefold over a field of characteristic zero and |L| be a base-point free, ample linear system on X. Under suitable hypotheses on (X, |L|), we prove that for a very general member Y ∈ |L|, the restriction map on divisor class groups Cl (X)→ Cl (Y ) is an isomorphism. In particular, we are able to recover the classical Noether-Lefschetz theorem, that a very general ...

A New Löwenheim-skolem Theorem

This paper establishes a refinement of the classical LöwenheimSkolem theorem. The main result shows that any first order structure has a countable elementary substructure with strong second order properties. Several consequences for Singular Cardinals Combinatorics are deduced from this.

A Noether-Deuring theorem for derived categories

We prove a Noether-Deuring theorem for the derived category of bounded complexes of modules over a Noetherian algebra.

Skolem Rings and Their Varieties