Ring of invariants of general linear group over local ring \mathbb{Z}_{p^m } |
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Authors: | Jizhu Nan Yin Chen |
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Institution: | 1. School of Mathematics Sciences, Dalian University of Technology, Dalian, 116024, China 2. School of Mathematics & Statistics, Northeast Normal University, Changchun, 130024, China
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Abstract: | Let
\mathbbZpm \mathbb{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
(
\mathbbZpm \mathbb{Z}_{p^m } ) acts naturally on the polynomial algebra A
n
:=
\mathbbZpm \mathbb{Z}_{p^m } x
1, …, x
n
]. Denote by
AnGL2 (\mathbbZpm ) A_n^{GL_2 (\mathbb{Z}_{p^m } )} 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. |
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Keywords: | |
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