零维理想的性质  

Properties of Zero-Dimensional Ideals

作　　者：李冬梅[1] 刘金旺[1] 

机构地区：[1]湖南科技大学数学与计算科学学院,湖南湘潭411201

出　　处：《湖南科技大学学报（自然科学版）》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)

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.

关 键 词：零维理想 素理想 准素理想 准素分解 

分 类 号：O153[理学—数学]