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| PIMD上一元多项式环的素理想分类 | |
| 引用本文： | 范志勇,张曙光,魏俊潮.PIMD上一元多项式环的素理想分类[J].河南师范大学学报(自然科学版),2012,40(4):16-19. |
| 作者姓名： | 范志勇 张曙光 魏俊潮 |
| 作者单位： | 1. 扬州大学数学科学学院,江苏扬州225002;焦作师范高等专科学校数学学院,河南焦作454002 2. 焦作师范高等专科学校数学学院,河南焦作,454002 3. 扬州大学数学科学学院,江苏扬州,225002 |
| 基金项目： | 国家自然科学基金，江苏省普通高校研究生科研创新项目，江苏省高校自然科学基金，河南省自然科学基金 |
| 摘 要： | 设R是主理想整环,若R有无穷多个极大理想,则称R是Principal Ideal Maximal Domain,简称为PIMD.设x是PIMD上的未定元,Rx]是R上的一元多项式环.依据整环的基本理论和唯一分解环的结构理论,研究Rx]的素理想和极大理想,推证了Rx]的任一主理想都不是极大理想,给出了构造Rx]的极大理想的一种方法,得到了Rx]的素理想是极大理想的条件,最终给出Rx]的素理想分类定理. |
| 关 键 词： | PIMD 一元多项式环 素理想 极大理想 |
Classification of the Prime Ideals of Polynomial Ring Over PIMD |
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| FAN Zhi-yong , ZHANG Shu-guang , WEI Jun-chao.Classification of the Prime Ideals of Polynomial Ring Over PIMD[J].Journal of Henan Normal University(Natural Science),2012,40(4):16-19. | |
| Authors: | FAN Zhi-yong ZHANG Shu-guang WEI Jun-chao |
| Institution: | 1(1.College of Mathematical science,Yangzhou University,Yangzhou 225002,China; 2.College of Mathematics,Jiaozuo Teachers College,Jiaozuo 454002,China) |
| Abstract: | Let R be a principal ideal domain.If R has infinite maximal ideals,then R is called a Principal Ideal Maximal Domain,for short,PIMD.Let x be an indeterminate over the PIMD R and Rx] denote the polynomial ring over R.In this thesis,according to the basic theory of domain and the structural theory of the unique factorization domain,we study the prime ideals and maximal ideals of Rx].We deduce that none of the principal ideal is maximal in Rx],and put forward a way to construct the maximal ideals of Rx],determine the conditions of prime ideals of Rx] as the maximal ideals,and ultimately confirme the classification of the prime ideals and maximal ideals of Rx]. |
| Keywords: | Principal Ideal Maximal Domain polynomial ring prime ideals maximal ideals |
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