Cogredient Standard Forms of Symmetric Matrices over Galois Rings of Odd Characteristic

Abstract EN

Let R=GR(ps,psm) be a Galois ring of characteristic ps and cardinality psm, where s and m are positive integers and p is an odd prime number.

Two kinds of cogredient standard forms of symmetric matrices over R are given, and an explicit formula to count the number of all distinct cogredient classes of symmetric matrices over R is obtained.