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1. Introduction. It seems highly appropriate to us that, in this address, 2 we should present to you results which represent new progress in the structure theory of associative division algebras, a field untouched for nearly thirty years, and which provided the topic of our doctoral dissertation of 1928. As in the paper already published, 8 we shall study the structure of a central division algebra 3), of odd prime degree p over any field ft of characteristic p, which has the property thatdoi:10.1090/s0002-9904-1968-11963-9 fatcat:tywmzut42ja4rkgkkxsznxokhm