摘要
主要研究和讨论多项式环k[x1,…,xn]中零维理想的一些性质及模零维理想I的商环k[x1,…,xn]/I可分解成一些无幂零元环的直和.并讨论了当I是准素理想、零维准素理想时,I∶f与I∶〈f1,…,fr〉的性质;得到了以下重要结论:当I是P-准素理想,则I∶〈f1,…,fr〉=R或是P-准素理想.参8.
Zero-dimensional ideals of polynomial ring k[x1,…,xn] were discussed. Some important properties of zero-dimensional ideals were obtained, and a result was gotten, which the residue class/ing of modulo a zero-dimensional ideal decomposed into the direct sum of some rings without nilpotent element. When 1 is a primary ideal or a zero-dimensional primary ideal,the properties of I：f and I：〈f1,…fr）are studied; and the important conclusion was gotten when 1 is a P- prime ideal, I：〈f1,…,fr〉 = R or is also a P- prime ideal. 8refs.
出处
《湖南科技大学学报（自然科学版）》
CAS
北大核心
2007年第4期126-128,共3页
Journal of Hunan University of Science And Technology：Natural Science Edition
基金
国家自然科学基金资助项目(10771058)
湖南省教育厅科研项目(06A017)
湖南省自然科学基金资助项目(06JJ2053)
关键词
零维理想
素理想
准素理想
准素分解
zero-dimensional ideal
prime ideal
primary ideal
primary decomposition
