Definite quadratic forms over Fq[x]

✍ Scribed by Larry J. Gerstein

• Book ID: 104140618
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 207 KB
• Volume: 268
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1016/s0021-8693(03)00114-5

✦ Synopsis

Let R be a principal ideal domain with quotient field F . An R-lattice is a free R-module of finite rank spanning an inner product space over F . The classification problem asks for a reasonably effective set of criteria to determine when two given R-lattices are isometric; that is, when there is an inner-product preserving isomorphism carrying one lattice onto the other. In this paper R is the polynomial ring F q [x], where F q is a finite field of odd order q. For F q [x]-lattices as for Z-lattices the theory splits into "definite" and "indefinite" cases, and this paper settles the classification problem in the definite case.