International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 1, Pages 89-95

Cyclotomic equations and square properties in rings

Benjamin Fine1,2

1Department of Mathematics, University of California Santa Barbara, Santa Barbara 93106, California, USA
2Department of Mathematics, Fairfield University, Fairfield 06430, Connecticut, USA

Received 5 May 1985

Copyright © 1986 Benjamin Fine. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.