Uniqueness of the Coefficient Ring in Some Group Rings
- 1 December 1973
- journal article
- Published by Canadian Mathematical Society in Canadian Mathematical Bulletin
- Vol. 16 (4) , 551-555
- https://doi.org/10.4153/cmb-1973-090-5
Abstract
Let 〈x〉 be an infinite cyclic group and Ri〈x〉 its group ring over a ring (with identity) Ri, for i = l and 2. Let J(Ri) be the Jacobson radical of Ri. In this note we study the question of whether or not R1〈x〉≃R2〈x〉 implies R1≃R2. We prove that this is so if Zi the centre of Ri is semi-perfect and J(Zi〈x〉) = J(Zi〈)x〉 for i = l and 2. In particular, when Zi is perfect the second condition is satisfied and the isomorphism of group rings Ri〈x〉 implies the isomorphism of Ri.Keywords
This publication has 2 references indexed in Scilit:
- R -Automorphisms of R [X ]Proceedings of the London Mathematical Society, 1968
- Radicals Of Polynomial RingsCanadian Journal of Mathematics, 1956