International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 1, Pages 89-95
Cyclotomic equations and square properties in rings
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 is a ring, the structure of the projective special linear group is used to investigate the existence of sum of square properties holding in . 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 where is a prime such that is not a square . Finally, it is shown that the class of sum of squares rings and the class satisfying square property one are non-coincidental.