Valuations and group algebras (Q1284625)

This paper discusses localization in group rings and crossed products of left ordered groups. To do this, the authors consider the following structure: (1) pairs \((\Gamma_1,\Pi_1)\) and \((\Gamma_2,\Pi_2)\) where \(\Pi_i\) is the positive cone of the left ordered group \(\Gamma_i\); (2) a subsemigroup \(\Delta\) of \(\Gamma_1\) containing \(\Pi_1\) and a cone preserving semigroup morphism \(\phi\colon\Delta\to\Gamma_2\). Since left ordered groups are unique product groups, the results of this paper concerning units, isomorphism questions and the Jacobson radical of crossed products are all well known.