Watts cohomology and separability

Andrew T. Kitchen

Vol. 42 (1972), No. 1, 99–104

DOI: 10.2140/pjm.1972.42.99

Abstract

A cohomology theory, H_K^pA, for commutative K-algebras, A, is discussed for the case where K is a field. This was originally introduced by C. E. Watts in connection with rings of continuous functions. N. Greenleaf computed H_K^pA in the case where A is an extension field of K. In this paper it is shown that, for any K-algebra A, the separable closure of K in A can be identified with H_K⁰A. Furthermore Greenleaf’s result is extended to a substantial class of local algebras.

Mathematical Subject Classification 2000

Primary: 18H10

Secondary: 13H05

Milestones

Received: 21 May 1971

Revised: 23 November 1971

Published: 1 July 1972