Anneaux de Krull non commutatifs

The discriminant controls automorphism groups of noncommutative algebras

Factorization theory: from commutative to noncommutative settings

Let be a compact -valued -adic Lie group, and let be its Iwasawa algebra. The present paper establishes results about the structure theory of finitely generated torsion -modules, up to pseudo-isomorphism, which are largely parallel to the classical theory when is abelian (except for basic differences which occur for those torsion modules which do not possess a non-zero global annihilator). We illustrate our general theory by concrete examples of such modules arising from the Iwasawa theory of elliptic curves without complex multiplication over the field generated by all of their -power torsion points.AMS 2000 Mathematics subject classification: Primary 11G05; 11R23; 16D70; 16E65; 16W70

Modules over iwasawa algebras

In this paper and a forthcoming joint one with Y. Hachimori we study Iwasawa modules over an infinite Galois extension K of a number field k whose Galois group G=G(K/k) is isomorphic to the semidirect product of two copies of the p-adic numbers. After first analyzing some general algebraic properties of the corresponding Iwasawa algebra, we apply these results to the Galois group of the p-Hilbert class field over K. \nAs a main tool we prove a Weierstrass preparation theorem for certain skew power series rings. One striking result in our work is the discovery of the abundance of faithful torsion modules, i.e. non-trivial torsion modules whose global annihilator ideal is zero. Finally we show that the completed group algebra with coefficients in the finite field of p elements is a unique factorization domain in the sense of Chatters.

https://www.degruyter.com/view/j/crll.2003.2003.issue-559/crll.2003.047/crll.2003.047.pdf

A non-commutative Weierstrass preparation theorem and applications to Iwasawa theory

(1992). Derivations et automorphismes de quelques algebras quantiques. Communications in Algebra: Vol. 20, No. 6, pp. 1787-1802.

Derivations et automorphismes de quelques algebras quantiques

(1978). 'Anneaux noetheriens a droite entiers sur un sous-anneau de leur centre' Communications in Algebra: Vol. 6, No. 2, pp. 203-222.

Marc Chamarie

Papers

Anneaux de Krull non commutatifs

Derivations et automorphismes de quelques algebras quantiques

"Anneaux noetheriens a droite entiers sur un sous-anneau de leur centre"

Localisations dans les ordres maximaux

Modules sur les anneaux de Krull non commutatifs