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Indexed by:期刊论文

Date of Publication:2011-10-01

Journal:FRONTIERS OF MATHEMATICS IN CHINA

Included Journals:Scopus、SCIE

Volume:6

Issue:5

Page Number:887-899

ISSN No.:1673-3452

Key Words:Dickson's theorem; invariant; finite local ring

Abstract:Let Z(p)(m) be the ring of integers modulo p(m), where p is a prime and m >= 1. The general linear group GL(n)( Z(p)(m)) acts naturally on the polynomial algebra A(n) := Z(p)(m)[x(1),..., x(n)]. Denote by A(n)(GLn(Zpm)) the corresponding ring of invariants. The purpose of the present paper is to calculate this invariant ring. Our results also generalize the classical Dickson's theorem.