摘要
本文用集合套为工具对Fuzzy环进行了重新刻划。主要讨论了以下问题:用集合套定义了Fuzzy环,Fuzzy理想,Fuzzy商环等概念,说明了这种定义与文献[4,5]中的定义是一致的,并讨论了一些基本性质,用集合套简便地证明了Fuzzy环的同态基本定理及有关的同构定理,不需要限制具有“sup”性质;最后研究了Fuzzy商子环和Fuzzy子环积的性质及同构定理.
In this paper the fuzzy rings are characterised again by the nested set and the following problems are discussed: using nested set to redefine the concepts of fuzzy rings, fuzzy ideals and fuzzy quotient rings and the definitions given are proved to be the same as in references[4,5],using nested set to prove in a simple way the homomorphism theorem and some isomorphic theorems in fuzzy rings, discussing the products of fuzzy rings and fuzzy quotient subrings.
关键词
模糊数学
集合套
FUZZY环
fuzzy mathematics,fuzzy ring,nested set,fuzzy ideal,fuzzy quotient ring, product of fuzzy subring.
