A bigger Brauer group

Abstract

Now A/ (J)A is a central separable algebra (Prop. 2.7) over the field R/ (J). It follows from Proposition 1.9 that A/ (J)A can have no proper nonzero regular ideals. Hence, if J is the image of J in A/ (J)A, then AJA -(0). We conclude that AJA c {J)A. Since (J)A c J and A 2 -A, it follows that AJA = (J)A, as claimed.