IJPAM: Volume 93, No. 6 (2014)

ON THE TYPICAL RANK OF REAL CLOSED FIELDS

E. Ballico
Department of Mathematics
University of Trento
38 123 Povo (Trento) - Via Sommarive, 14, ITALY


Abstract. In this note we introduce the notion of typical rank for any real closed field $R$, mimicking the case $R =\mathbb {R}$. We show that the typical ranks are the same if we take a larger real closed field and in particular that for every format $(n_1,\dots ,n_s)$ the typical ranks of tensors of format $(n_1,\dots ,n_s)$ are the same over $R$ and over $\mathbb {R}$.

Received: February 26, 2014

AMS Subject Classification: 14N05

Key Words and Phrases: typical rank, real closed field

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DOI: 10.12732/ijpam.v93i6.6 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 93
Issue: 6
Pages: 803 -

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).