Edinburgh Research Explorer

How far can we go with Amitsur's conjecture in differential polynomial rings?

Research output: Contribution to journalArticlepeer-review

Related Edinburgh Organisations

Open Access permissions



Original languageEnglish
Pages (from-to)555-608
Number of pages47
JournalIsrael journal of mathematics
Issue number2
Early online date12 May 2017
Publication statusE-pub ahead of print - 12 May 2017


A well-known theorem by S.A. Amitsur shows that the Jacobson radical of the polynomial ring R[x] equals I[x] for some nil ideal I of R. In this paper, however, we show that this is not the case for differential polynomial rings, by proving that there is a ring R which is not nil and a derivation D on R such that the differential polynomial ring R[x;D] is Jacobson radical. We also show that, on the other hand, the Amitsur theorem holds for a differential polynomial ring R[x;D], provided that D is a locally nilpotent derivation and R is an algebra over a field of characteristic p > 0. The main idea of the proof introduces a new way of embedding differential polynomial rings into bigger rings, which we name platinum rings, plus a key part of the proof involves the solution of matrix theory-based problems.

Download statistics

No data available

ID: 25272830