Cyclotomic equations and square properties in rings. (1986) - Fine, Benjamin
Abstract : IfR is a ring, the structure of the projective special linear groupPSL 2 ( R ) is used to investigate the existence of sum of square properties holding inR . 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 andZ p n whereP is a prime such that− 3 is not a squaremod p . Finally, it is shown that the class of sum of squares rings and the class satisfying square property one are non-coincidental.