[1]马 宁,彭国华*.有限交换环上的Chowla定理[J].四川师范大学学报(自然科学版),2018,(03):296-298.[doi:10.3969/j.issn.1001-8395.2018.03.002]
 MA Ning,PENG Guohua.On Chowla's Theorem over Finite Commutative Rings[J].Journal of SichuanNormal University,2018,(03):296-298.[doi:10.3969/j.issn.1001-8395.2018.03.002]
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有限交换环上的Chowla定理()
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2018年03期
页码:
296-298
栏目:
基础理论
出版日期:
2018-03-15

文章信息/Info

Title:
On Chowla's Theorem over Finite Commutative Rings
文章编号:
1001-8395(2018)03-0296-03
作者:
马 宁 彭国华*
四川大学 数学学院, 四川 成都 610064
Author(s):
MA Ning PENG Guohua
College of Mathematics, Sichuan University, Chengdu 610064, Sichuan
关键词:
完全剩余系 有限交换环 M-环 置换多项式
Keywords:
complete residue system finite commutative ring M-ring permutation polynomial
分类号:
O15
DOI:
10.3969/j.issn.1001-8395.2018.03.002
文献标志码:
A
摘要:
设R={r0,r1,…,rn-1}是一个有限含幺交换环,若对于r0,r1,…,rn-1的任意排列s0,s1,…,sn-1都有{risi|0≤i≤n-1}≠R,则称R为M-环.讨论了M-环的基本性质,利用有限交换环的结构定理,得到了R为M-环的判定条件.这些结论将整数环上关于剩余系的Chowla定理推广到M-环上,进而统一证明了Chowla定理以及孙琦和旷京华给出的代数整数环上的Chowla定理.此外还给出有限交换环上置换多项式一个结论的简单证明.
Abstract:
A finite commutative ring R={r0,r1,…,rn-1} with identity is called an M-ring, if {risi|0≤i≤n-1}≠R holds for every arrangement s0,s1,…,sn-1 of r0,r1,…,rn-1. We discuss the basic properties of M-rings, and give a simple characteristic of these rings basing on the structure properties of finite commutative rings. Our results generalize Chowla's Theorem on residue class rings over integers to M-rings, and then integrate a similar result on the residue class ring associated to a Dedekind domain given by Sun and Kuang. Moreover, we give a simple proof for a result on permutation polynomials over M-rings.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2017-04-23 接受日期:2017-05-15
基金项目:国家自然科学基金(11171150)
*通信作者简介:彭国华(1967—),男,教授,主要从事数论和密码学的研究,E-mail:peng@scu.edu.cn
更新日期/Last Update: 2018-03-15