Lifting to non-integral idempotents

In the first section of this paper, we illustrate (for a finite group G and the field of fractions image of a suitable complete dvr R) how to produce all central idempotents of image from knowledge of the images of Z(RG) modulo certain powers of J(R). In the second section, we outline another approach to lifting elements closely related to idempotents in more general rings, which may be of wider interest.