A noncommutative real nullstellensatz corresponds to a noncommutative real ideal: Algorithms

作者：Cimpric Jakob^*; Helton J William; McCullough Scott; Nelson Christopher

来源：Proceedings of the London Mathematical Society, 2013, 106: 1060-1086.

DOI：10.1112/plms/pds060

First, we introduce notions of the (noncommutative) zero set of a left ideal and of a real left ideal. We prove that every element from R %26lt;%26lt; x, x* %26gt;%26gt; whose zero set contains the intersection of zero sets of elements from a finite subset S of R %26lt;%26lt; x, x* %26gt;%26gt; belongs to the smallest real left ideal containing S. %26lt;br%26gt;Next, we give an implementable algorithm, which for every finite S subset of R %26lt;%26lt; x, x* %26gt;%26gt;, computes the smallest real left ideal containing S, and prove that the algorithm succeeds in a finite number of steps. %26lt;br%26gt;Our definitions and some of our results also work for other *-algebras. As an example, we treat real left ideals in M-n(R[x(1)]).

• 出版日期2013-5