Noether-FI代数与Artin-FI代数  

Noether and Artin FI-algebras

作　　者：刘春辉[1] LIU Chun-hui(Department of Mathematics and Statistics,Chifeng University,Chifeng 024001,China)

机构地区：[1]赤峰学院数学与统计学院

出　　处：《数学的实践与认识》2018年第20期173-178,共6页Mathematics in Practice and Theory

基　　金：内蒙古自治区高等学校科学研究项目(NJSY14238)

摘　　要：以滤子概念为工具研究FI代数的结构问题．基于脚滤子升链族和降链族引入了Noether—FI代数与Artin-FI代数的概念，并利用御滤子和模糊MP滤子的性质获得了Noether—FI代数与Artin—FI代数若干等价刻画．为进一步深入研究FI代数提供了一个有力工具．In this paper, we study the structural problem of FI-algebras by using the concept of MP-filters. The concepts of Noether FI-algebra and Artin FI-algebra are introduced based on MP-filter ascending chain and descending chain family. By using the properties of MP- filters and fuzzy MP-filters, some equivalent characterizations of Noether FI-algebras and Artin FI-algebras are obtained. It gives us a powerful tool for the further study of the FI-algebras.

关 键 词：模糊逻辑 FI代数 MP滤子 Noether-FI代数 Artin-FI代数 

分 类 号：O159[理学—数学]