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The Critical Set of the Reduced Norm, as an Algebraic Set

Don Goelman
Proceedings of the American Mathematical Society
Vol. 48, No. 2 (Apr., 1975), pp. 307-312
DOI: 10.2307/2040259
Stable URL: http://www.jstor.org/stable/2040259
Page Count: 6
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
The Critical Set of the Reduced Norm, as an Algebraic Set
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Abstract

For an associative algebra A over k, the reduced norm ν: A → k is a polynomial function. As such the critical set Cν is defined, consisting of points where the differential (dν)z vanishes. The k-rational points of Cν 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 Cν as an algebraic k-set is discussed.

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