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The critical set of the reduced norm, as an algebraic set

Author: Don Goelman
Journal: Proc. Amer. Math. Soc. 48 (1975), 307-312
MSC: Primary 14A25
MathSciNet review: 0364239
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Abstract: For an associative algebra $ A$ over $ k$, the reduced norm $ \nu :A \to k$ is a polynomial function. As such the critical set $ {C_\nu }$ is defined, consisting of points where the differential $ {(d\nu )_z}$ vanishes. The $ k$-rational points of $ {C_\nu }$ have been determined by the author under certain separability conditions (Rational critical points of the reduced norm of an algebra, Bull. Amer. Math. Soc. 80 (1974), 138-141); here the dimension of $ {C_\nu }$ as an algebraic $ k$-set is discussed.

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Keywords: Reduced norm, critical set, central simple algebra
Article copyright: © Copyright 1975 American Mathematical Society

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