Cyclotomic equations and square properties in rings

Benjamin Fine

International Journal of Mathematics and Mathematical Sciences, 1986, vol. 9, 1-7

Abstract:

If R is a ring, the structure of the projective special linear group PSL 2 ( R ) is used to investigate the existence of sum of square properties holding in R . Rings which satisfy Fermat's two-square theorem are called sum of squares rings and have been studied previously. The present study considers a related property called square property one. It is shown that this holds in an infinite class of rings which includes the integers, polynomial rings over many fields and Z p n where P is a prime such that − 3 is not a square mod p . Finally, it is shown that the class of sum of squares rings and the class satisfying square property one are non-coincidental.

Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:831935

DOI: 10.1155/S016117128600011X

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