A Model Theoretic Perspective of Matrix Rings

Marcus Tressl; Igor Klep

A Model Theoretic Perspective of Matrix Rings

Marcus Tressl, Igor Klep

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Number of pages	20
Journal	Advances in Mathematics
Publication status	Submitted - 2 Nov 2018
Externally published	Yes

Keywords

Model theory, quantifier elimination, matrix rings, decida bility, free analysis, invariant theory

Cite this

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AU - Klep, Igor

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AB - 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.

KW - Model theory, quantifier elimination, matrix rings, decida bility, free analysis, invariant theory

UR - https://arxiv.org/abs/1810.09024

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SN - 0001-8708

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

A Model Theoretic Perspective of Matrix Rings

Abstract

Keywords

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