Vol. 97, No. 1, 1981

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Sums of squares in planar Nash rings

Gustave Adam Efroymson

Vol. 97 (1981), No. 1, 75–79
Abstract

In a previous paper, the author developed the ideal theory of Nash rings on planar domains. Here that theory is applied to show that a Nash function on a planar domain D which takes on only non-negative values on D is a sum of two squares of Nash functions on D. Examples are given which clarify the situation for higher dimensions.

Mathematical Subject Classification 2000
Primary: 12D99
Secondary: 13B02, 32B99, 14G30, 10C04
Milestones
Received: 10 July 1980
Published: 1 November 1981
Authors
Gustave Adam Efroymson