Submission date: 21 October 2018

Abstract:

Quantifier elimination of matrix rings M_n(K) for K a formally real field is characterized in the language of rings extended by trace and transposition, in terms of invariant theory. This is used to prove quantifier elimination when K is an intersection of real closed fields. For dimension-free matrices it is shown that no such result can hold by establishing various undecidability results.

Mathematics Subject Classification: 03C10, 16R30, 16W22, 15A21

Keywords and phrases:

Full text arXiv 1810.09024: pdf, ps.