CONGRUENCE OF SYMMETRIC INNER PRODUCTS OVER FINITE COMMUTATIVE RINGS OF ODD CHARACTERISTIC
2017 ◽
Vol 96
(3)
◽
pp. 389-397
Keyword(s):
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.
2019 ◽
Vol 19
(12)
◽
pp. 2050226
◽
Keyword(s):
2019 ◽
Vol 19
(09)
◽
pp. 2050173
2018 ◽
Vol 17
(07)
◽
pp. 1850121
Keyword(s):
2012 ◽
Vol 11
(06)
◽
pp. 1250103
◽
Keyword(s):
2015 ◽
Vol 07
(01)
◽
pp. 1450064
◽
2018 ◽
Vol 17
(03)
◽
pp. 1850054
◽
2013 ◽
Vol 12
(04)
◽
pp. 1250199
◽
2011 ◽
Vol 10
(04)
◽
pp. 665-674
Keyword(s):