Artin IS-代数的特征

Characterizations of Artin IS-algebras

引入ArtinIS-代数的概念,利用反模糊理想,刻划ArtinIS-代数的特征,得到如下结论:①设X是ArtinIS-代数且μ是X的一个反模糊理想,若Imμ的元素序列是严格递减的,则μ有有限值;②若IS-代数X的任意模糊理想有有限值,则X是Artin的.

The purpose of this paper is to provide characterizations of Artin IS - algebras in term of anti - fuzzy ideals and to obtain the main results；①Let X be an Artin IS-algebra and μ an anti - fuzzy ideal of X. If a sequence of elements of Imμ is strictly increasing, then μ has finite number of values ; ② let X be an IS - algebra. If every anti-fuzzy ideals of X has finite number of values, then X is Artin.