Submission: 2010, Dec 9
We show that a pythagorean field (more generally, a reduced abstract Witt ring) has finite stability index if and only if it has finite $2$-symbol length. We give explicit bounds for the two invariants in terms of one another. To approach the question whether those bounds are optimal we consider examples of pythagorean fields.
2010 Mathematics Subject Classification: 11E04, 11E10, 11E81
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