Cyclotomic equations and square properties in rings. (1986)

• Record Type: Journal Article
• Authors: Fine, Benjamin
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 9:Number 1(1986)
• Page Start: 89
• Page End: 95
• Publication Date: 1986
• Subjects: Fermat's two square theorem -- PSL 2 (R) -- trace class -- sum of squares ring -- modular group -- free product of groups; Mathematics -- Periodicals; 510.5
• DOI: 10.1155/S016117128600011X
• Languages: English
• ISSNs: 0161-1712

Abstract

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.