A Real Holomorphy Ring without the Schmüdgen Property

Canadian mathematical bulletin

关键词: HNN-extension;    nilpotent groups;    cyclic subgroup separable $(pi_c)$;    residually finite;   

DOI  :  10.4153/CMB-1999-041-2

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

A preordering $T$ is constructed in the polynomial ring $A = R[t_1,t_2, dots]$ (countably many variables) with the following twoproperties: (1)~~For each $f in A$ there exists an integer $N$such that $-N le f(P) le N$ holds for all $P in Sper_T(A)$.(2)~~For all $f in A$, if $N+f, N-f in T$ for some integer $N$,then $f in R$. This is in sharp contrast with theSchm"udgen-W"ormann result that for any preordering $T$ in afinitely generated $R$-algebra $A$, if property~(1) holds, thenfor any $f in A$, $f > 0$ on $Sper_T(A) Rightarrow f in T$.Also, adjoining to $A$ the square roots of the generators of $T$yields a larger ring $C$ with these same two properties but with$Sigma C^2$ (the set of sums of squares) as the preordering.

【 授权许可】

Unknown