International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 1, Pages 89-95
doi:10.1155/S016117128600011X

Cyclotomic equations and square properties in rings

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.