有限特征域上忠实同态的构造

IF 0.8 Q3 COMPUTER SCIENCE, THEORY & METHODS ACM Transactions on Computation Theory Pub Date : 2018-12-26 DOI:10.1145/3580351
Prerona Chatterjee, Ramprasad Saptharishi
{"title":"有限特征域上忠实同态的构造","authors":"Prerona Chatterjee, Ramprasad Saptharishi","doi":"10.1145/3580351","DOIUrl":null,"url":null,"abstract":"We study the question of algebraic rank or transcendence degree preserving homomorphisms over finite fields. This concept was first introduced by Beecken et al. [3] and exploited by them, and Agrawal et al. [2] to design algebraic independence–based identity tests using the Jacobian criterion over characteristic zero fields. An analogue of such constructions over finite characteristic fields was unknown due to the failure of the Jacobian criterion over finite characteristic fields. Building on a recent criterion of Pandey et al. [15], we construct explicit faithful maps for some natural classes of polynomials in the positive characteristic field setting, when a certain parameter called the inseparable degree of the underlying polynomials is bounded (this parameter is always 1 in fields of characteristic zero). This presents the first generalisation of some of the results of Beecken et al. [3] and Agrawal et al. [2] in the positive characteristic setting.","PeriodicalId":44045,"journal":{"name":"ACM Transactions on Computation Theory","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2018-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Constructing Faithful Homomorphisms over Fields of Finite Characteristic\",\"authors\":\"Prerona Chatterjee, Ramprasad Saptharishi\",\"doi\":\"10.1145/3580351\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the question of algebraic rank or transcendence degree preserving homomorphisms over finite fields. This concept was first introduced by Beecken et al. [3] and exploited by them, and Agrawal et al. [2] to design algebraic independence–based identity tests using the Jacobian criterion over characteristic zero fields. An analogue of such constructions over finite characteristic fields was unknown due to the failure of the Jacobian criterion over finite characteristic fields. Building on a recent criterion of Pandey et al. [15], we construct explicit faithful maps for some natural classes of polynomials in the positive characteristic field setting, when a certain parameter called the inseparable degree of the underlying polynomials is bounded (this parameter is always 1 in fields of characteristic zero). This presents the first generalisation of some of the results of Beecken et al. [3] and Agrawal et al. [2] in the positive characteristic setting.\",\"PeriodicalId\":44045,\"journal\":{\"name\":\"ACM Transactions on Computation Theory\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2018-12-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACM Transactions on Computation Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3580351\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACM Transactions on Computation Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3580351","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 1

摘要

研究有限域上代数保秩或保超越度同态的问题。这个概念首先由Beecken等人提出,并被他们利用,Agrawal等人利用特征零域上的雅可比准则设计了基于代数独立性的恒等检验。由于雅可比准则在有限特征场上的失效,这种结构在有限特征场上的模拟是未知的。在Pandey et al.[15]的最新准则的基础上,我们构造了一些自然多项式类在正特征域设置中的显式忠实映射,当某个参数称为底层多项式的不可分度是有界的(该参数在特征为零的域中总是1)。这是Beecken et al.[3]和Agrawal et al.[2]在正特征设置下的一些结果的首次推广。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
Constructing Faithful Homomorphisms over Fields of Finite Characteristic
We study the question of algebraic rank or transcendence degree preserving homomorphisms over finite fields. This concept was first introduced by Beecken et al. [3] and exploited by them, and Agrawal et al. [2] to design algebraic independence–based identity tests using the Jacobian criterion over characteristic zero fields. An analogue of such constructions over finite characteristic fields was unknown due to the failure of the Jacobian criterion over finite characteristic fields. Building on a recent criterion of Pandey et al. [15], we construct explicit faithful maps for some natural classes of polynomials in the positive characteristic field setting, when a certain parameter called the inseparable degree of the underlying polynomials is bounded (this parameter is always 1 in fields of characteristic zero). This presents the first generalisation of some of the results of Beecken et al. [3] and Agrawal et al. [2] in the positive characteristic setting.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
ACM Transactions on Computation Theory
ACM Transactions on Computation Theory COMPUTER SCIENCE, THEORY & METHODS-
CiteScore
2.30
自引率
0.00%
发文量
10
期刊最新文献
Small-Space Spectral Sparsification via Bounded-Independence Sampling Tight Sum-of-Squares lower bounds for binary polynomial optimization problems Optimal Polynomial-time Compression for Boolean Max CSP On p -Group Isomorphism: search-to-decision, counting-to-decision, and nilpotency class reductions via tensors Quantum communication complexity of linear regression
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1