Homogeneous Stellensätze in semialgebraic geometry

Guangxin Zeng

Vol. 136 (1989), No. 1, 103–122

DOI: 10.2140/pjm.1989.136.103

Abstract

In this paper, we introduce homogeneous (U,W)-radical ideals of a commutative graded ring A with 1, where both U and W are two multiplicative subsemigroups of homogeneous elements in A such that U ⊆ W, and apply these results to prove the homogeneous semialgebraic Stellensätze. Finally, we investigate some quantitative aspects related to these Stellensätze, and Problem 2 posed by G. Stengle is answered affirmatively as a special example.

Mathematical Subject Classification 2000

Primary: 14P10

Secondary: 12J15

Milestones

Received: 20 July 1987

Revised: 8 April 1988

Published: 1 January 1989