FUZZY IDEALS OF ARTINIAN-RINGS

被引：22
|
作者：
MALIK, DS
机构：
[1] Department of Mathematics and Computer Science, Creighton University, Omaha
来源：
FUZZY SETS AND SYSTEMS | 1990年 / 37卷 / 01期
关键词：
Artinian ring; Fuzzy ideal; fuzzy module; ideal; module; Noetherian ring; level ideal;
D O I：
10.1016/0165-0114(90)90069-I
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
The object of this paper is to study fuzzy ideals over Artinian rings. Among others we prove that a ring with unity is left (right) Artinian if and only if every fuzzy left (right) ideal μ of R is finite valued. This gives a characterization of artinian rings in terms of fuzzy ideals. Mukherjee and Sen (1987) proved that if every fuzzy ideal of a ring with unity is finite valued then the ring is Noetherian. We give an example to show that the converse of this theorem is not true. We also show that certain results of Pan (1987) are not true. © 1990.
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页码：111 / 115
页数：5
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