Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2011-10-01

Journal: FRONTIERS OF MATHEMATICS IN CHINA

Included Journals: SCIE、Scopus

Volume: 6

Issue: 5

Page Number: 887-899

ISSN: 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.