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CONGRUENCE OF SYMMETRIC INNER PRODUCTS OVER FINITE COMMUTATIVE RINGS OF ODD CHARACTERISTIC
Published online by Cambridge University Press: 08 June 2017
Abstract
Let $R$ be a finite commutative ring of odd characteristic and let $V$ be a free $R$-module of finite rank. We classify symmetric inner products defined on $V$ up to congruence and find the number of such symmetric inner products. Additionally, if $R$ is a finite local ring, the number of congruent symmetric inner products defined on $V$ in each congruence class is determined.
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 96 , Issue 3 , December 2017 , pp. 389 - 397
- Copyright
- © 2017 Australian Mathematical Publishing Association Inc.