Sweedler's two-cocycles and generalizations of theorems on Amitsur cohomology

Author:
Dave Riffelmacher

Journal:
Trans. Amer. Math. Soc. **251** (1979), 255-265

MSC:
Primary 16A62

DOI:
https://doi.org/10.1090/S0002-9947-1979-0531978-7

MathSciNet review:
531978

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Abstract: For any (not necessarily commutative) algebra *C* over a commutative ring *k* Sweedler defined a cohomology set, denoted here by , which generalizes Amitsur's second cohomology group . In this paper, if *I* is a nilpotent ideal of *C* and is *K*-projective, a natural bijection is established. Also, when are fields and *C* is a commutative *B*-algebra, the sequence is shown to be exact if the natural map induces a surjection on units, is induced by the inclusion, and *r* is the ``restriction'' map.

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DOI:
https://doi.org/10.1090/S0002-9947-1979-0531978-7

Article copyright:
© Copyright 1979
American Mathematical Society