Projects per year
Abstract
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.
Original language | English |
---|---|
Pages (from-to) | 555-608 |
Number of pages | 47 |
Journal | Israel journal of mathematics |
Volume | 219 |
Issue number | 2 |
DOIs | |
Publication status | Published - 12 May 2017 |
Fingerprint
Dive into the research topics of 'How far can we go with Amitsur's conjecture in differential polynomial rings?'. Together they form a unique fingerprint.Projects
- 1 Finished
Profiles
-
Agata Smoktunowicz
- School of Mathematics - Personal Chair in Algebra
Person: Academic: Research Active