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A Dimension Theorem for Real Primes

Published online by Cambridge University Press:  20 November 2018

D. Dubois  and
G. Efroymson
D. Dubois
Affiliation:
University of New Mexico, Albuquerque, New Mexico
G. Efroymson
Affiliation:
University of New Mexico, Albuquerque, New Mexico
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Let k be a real closed field (see § 2 for a definition). Let be an algebraic closure of k. An algebraic set denned over k is, as usual, a subset of (n some integer greater than 0) which is the set of zeros of some polynomials in k[X1, . . . , Xn]. A variety is denned to be an absolutely irreducible algebraic set. We define the real points of an algebraic set X to be the points in X ∩ kn. One can then define X to be real if I(X ∩ kn) = I(X). (I(X) = the polynomials in k[X1, . . . , Xn] which vanish on X.)

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 1 , February 1974 , pp. 108 - 114
Copyright
Copyright © Canadian Mathematical Society 1974

References

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