| Naslov: | A model theoretic perspective on matrix rings |
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| Avtorji: | ID Klep, Igor (Avtor)
ID Tressl, Marcus (Avtor) |
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| Datoteke: |  PDF - Predstavitvena datoteka, prenos (367,37 KB)
MD5: 19E4713AD70D9254F5E994F5C3041E9D
 URL - Izvorni URL, za dostop obiščite https://link.springer.com/article/10.1007/s00209-024-03671-w
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| Jezik: | Angleški jezik |
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| Tipologija: | 1.01 - Izvirni znanstveni članek |
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| Organizacija: |  IMFM - Inštitut za matematiko, fiziko in mehaniko
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| Povzetek: | In this paper natural necessary and sufficient conditions for quantifier elimination of matrix rings $M_n(K)$ in the language of rings expanded by two unary functions, naming the trace and transposition, are identified. This is used together with invariant theory to prove quantifier elimination when $K$ is an intersection of real closed fields. On the other hand, it is shown that finding a natural definable expansion with quantifier elimination of the theory of $M_n({\mathbb C})$ is closely related to the infamous simultaneous conjugacy problem in matrix theory. Finally, for various natural structures describing dimension-free matrices it is shown that no such elimination results can hold by establishing undecidability results. |
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| Ključne besede: | model theory, quantifier elimination, matrix rings, trace, decidability, free analysis, simultaneous conjugacy problem |
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| Status publikacije: | Objavljeno |
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| Verzija publikacije: | Objavljena publikacija |
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| Datum objave: | 01.03.2025 |
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| Leto izida: | 2025 |
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| Št. strani: | 20 str. |
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| Številčenje: | Vol. 309, iss. 3, article no. 45 |
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| PID: | 20.500.12556/DiRROS-23892  |
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| UDK: | 512 |
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| ISSN pri članku: | 0025-5874 |
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| DOI: | 10.1007/s00209-024-03671-w |
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| COBISS.SI-ID: | 225046275 |
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| Datum objave v DiRROS: | 20.10.2025 |
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| Število ogledov: | 193 |
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| Število prenosov: | 87 |
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| Metapodatki: |    |
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