Vol. 42, No. 1, 1972

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Watts cohomology and separability

Andrew T. Kitchen

Vol. 42 (1972), No. 1, 99–104

A cohomology theory, HKpA, 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 HKpA 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 HK0A. Furthermore Greenleaf’s result is extended to a substantial class of local algebras.

Mathematical Subject Classification 2000
Primary: 18H10
Secondary: 13H05
Received: 21 May 1971
Revised: 23 November 1971
Published: 1 July 1972
Andrew T. Kitchen