Difference between revisions of "Formally real field"
From Encyclopedia of Mathematics
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====References==== | ====References==== | ||
| − | * Tsit Yuen Lam, ''Introduction to Quadratic Forms over Fields'', Graduate Studies in Mathematics '''67''', American Mathematical Society (2005) ISBN 0-8218-1095-2 {{ZBL|1068.11023}} {{MR|2104929 }} | + | * Tsit Yuen Lam, ''Introduction to Quadratic Forms over Fields'', Graduate Studies in Mathematics '''67''', American Mathematical Society (2005) {{ISBN|0-8218-1095-2}} {{ZBL|1068.11023}} {{MR|2104929 }} |
| − | * A. R. Rajwade, ''Squares'', London Mathematical Society Lecture Note Series '''171''' Cambridge University Press (1993) ISBN 0-521-42668-5 {{ZBL|0785.11022}} | + | * A. R. Rajwade, ''Squares'', London Mathematical Society Lecture Note Series '''171''' Cambridge University Press (1993) {{ISBN|0-521-42668-5}} {{ZBL|0785.11022}} |
| − | * J.W. Milnor, D. Husemöller, ''Symmetric bilinear forms'', Ergebnisse der Mathematik und ihrer Grenzgebiete '''73''', Springer-Verlag (1973) ISBN 0-387-06009-X {{ZBL|0292.10016}} | + | * J.W. Milnor, D. Husemöller, ''Symmetric bilinear forms'', Ergebnisse der Mathematik und ihrer Grenzgebiete '''73''', Springer-Verlag (1973) {{ISBN|0-387-06009-X}} {{ZBL|0292.10016}} |
Latest revision as of 15:08, 15 August 2023
2020 Mathematics Subject Classification: Primary: 12J15 [MSN][ZBL]
A field $F$ which is capable of being made an ordered field. The existence of such an order is equivalent to the property that $-1$ is not a sum of squares in $F$: this is the Artin--Schreier theorem. A real closed field is a formally real field for which no algebraic extension is formally real.
References
- Tsit Yuen Lam, Introduction to Quadratic Forms over Fields, Graduate Studies in Mathematics 67, American Mathematical Society (2005) ISBN 0-8218-1095-2 Zbl 1068.11023 MR2104929
- A. R. Rajwade, Squares, London Mathematical Society Lecture Note Series 171 Cambridge University Press (1993) ISBN 0-521-42668-5 Zbl 0785.11022
- J.W. Milnor, D. Husemöller, Symmetric bilinear forms, Ergebnisse der Mathematik und ihrer Grenzgebiete 73, Springer-Verlag (1973) ISBN 0-387-06009-X Zbl 0292.10016
How to Cite This Entry:
Formally real field. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Formally_real_field&oldid=35479
Formally real field. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Formally_real_field&oldid=35479