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The Critical Set of the Reduced Norm, as an Algebraic Set
Proceedings of the American Mathematical Society
Vol. 48, No. 2 (Apr., 1975), pp. 307-312
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2040259
Page Count: 6
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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.
Proceedings of the American Mathematical Society © 1975 American Mathematical Society