On quotients of generalized Euclidean group rings

Abstract

Let $R=Z[C]$ be the integral group ring of a finite cyclic group $C$. Dennis and al. proved that $R$ is a generalized Euclidean ring in the sense of P. M. Cohn, i.e., $S{L}_n(R)$ is generated by the elementary matrices for all $n$. We prove that every proper quotient of $R$ is also a generalized Euclidean ring.

arXiv comment6 pages, no figure. Modification: fixed typo in assertion (iii) of Lemma 1 (thanks to Emom)