Projective modules over Laurent polynomial rings

Projecttve Modules over Laurent Polynomial Rings

Quillen's solution of Serre's problem is extended to Laurent polynomial rings. An example is given of a A[T, r~']-module P which is not extended even though A is regular and Pm is extended for all maximal ideals m of A. The object of this note is to present several comments and examples related to some problems suggested by Quillen's recent solution of Serre's problem [7]. It is an immediate co...

On modules over Laurent polynomial rings

A finitely generated Λ = Z[t, t]-module without Z-torsion is determined by a pair of sub-lattices of Λ. Their indices are the absolute values of the leading and trailing coefficients of the order of the module. This description has applications in knot theory. MSC 2010: Primary 13E05, 57M25.

Projective modules over polynomial rings and dynamical Gröbner bases

Modules over Differential Polynomial Rings

This note announces a number of results on the structure of differential modules over differential rings, where differential ring means a ring with a family of derivations and differential module means a module having a family of operators compatible with the derivations of the ring. To fix notation, throughout the paper we let A denote an associative ring, M = AM an 4-module, k the correspondi...

Generalized Laurent Polynomial Rings as Quantum Projective 3-spaces

Given a ring R, we introduce the notion of a generalized Laurent polynomial ring over R. This class includes the generalized Weyl algebras. We show that these rings inherit many properties from the ground ring R. This construction is then used to create two new families of quadratic global dimension four Artin-Schelter regular algebras. We show that in most cases the second family has a finite ...