JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and… (More)

The present paper lays no claim to deep originality. Its main purpose is to give a systematic treatment of the methods by which topological questions concerning compact Lie groups may be reduced to… (More)

THE EXCEPTIONAL SIMPLE LIE ALGEBRAS F4 AND E6 By CLAUDE CHEVALLEY AND R. D. SCHAFER DEPARTMENTS OF MATHEMATICS, COLUMBIA UNIVERSITY AND UNIVERSITY OF PENNSYLVANIA Communicated by A. A. Albert,… (More)

After a long illness Élie Cartan died on May 6, 1951, in Paris. His death came at a time when his reputation and the influence of his ideas were in full ascent. Undoubtedly one of the greatest… (More)

This paper is aimed at exhibiting two striking features of the usual approach of emotional expression in science and philosophy, suggesting a different perspective. One is the generally shared belief… (More)

Let K/k, K'/k be two extensions of a basic field k. By a composite extension of these two extensions, we understand the complex notion formed of an extension §t/k of k, of an isomorphism r of K/k… (More)

versely if the first row is multiplied by the inverse of c (mod p). This inverse exists, and the correspondence is one-to-one, because c is prime to p. This proves (3). The sum of the probabilities… (More)