Noether-FI代数与Artin-FI代数

Noether and Artin FI-algebras

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.