Abstract
If R is a ring, the structure of the projective special linear group PSL2(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 Zpn where P is a prime such that −3 is not a square modp. Finally, it is shown that the class of sum of squares rings and the class satisfying square property one are non‐coincidental.
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