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(∈,∈∨q)-模糊正规化子与(∈,∈∨q)-模糊商子群
引用本文:姚炳学.(∈,∈∨q)-模糊正规化子与(∈,∈∨q)-模糊商子群[J].吉首大学学报(自然科学版),2003,24(2):23-25.
作者姓名:姚炳学
作者单位:(聊城大学数学与系统科学系,山东 聊城252059)
基金项目:山东省自然科学基金资助项目(Y2000A05)
摘    要:在(∈,∈∨q)-模糊子群的基础上,引入了(∈,∈∨q)-模糊正规化子与(∈,∈∨q)-模糊中心化子的概念,并讨论了它们的一些性质.同时,给出了(∈,∈∨q)-模糊商群与(∈,∈∨q)-模糊商子群的定义,建立了(∈,∈∨q)-模糊商群的同构定理.

关 键 词:(∈∈∨q)-子群  (∈∈∨q)-模糊正规子群  (∈∈∨q)-模糊正规化子  (∈∈∨q)-模糊中心化子  (∈∈∨q)-模糊商子群

(∈,∈∨q)-Fuzzy Normalizer and (∈,∈∨q)-Fuzzy Quotient Subgroup
YAO,Bing-Xue.(∈,∈∨q)-Fuzzy Normalizer and (∈,∈∨q)-Fuzzy Quotient Subgroup[J].Journal of Jishou University(Natural Science Edition),2003,24(2):23-25.
Authors:YAO  Bing-Xue
Institution:(Department of Mathematics and System Science,Liaocheng University,Liaocheng 252059,Shandong China)
Abstract:Based on the concept of (∈,∈∨q)-fuzzy subgroup introduced by S.K.Bhakat in 1992,the notions of  (∈,∈∨q)- fuzzy normalizer and (∈,∈∨q)-fuzzy centralizer are introduced.Some properties of (∈,∈∨q)-fuzzy normalizer and (∈,∈∨q)- fuzzy centralizer are discussed.Then,the definition of(∈,∈∨q)- fuzzy quotient group and (∈,∈∨q)-fuzzy quotient subgroup is given.At last,the isomorphism theorem for (∈,∈∨q)-fuzzy quotient group is established.The main results include:(1)if is a fuzzy subset of,then the (∈,∈∨q)-fuzzy normalizer of is a subgroup of;(2)if is a fuzzy subgroup of,then the (∈,∈∨q)-fuzzy centralizer of is a subgroup of and a normal subgroup of;(3)if and are (∈,∈∨q)-fuzzy normal subgroup and (∈,∈∨q)-fuzzy subgroup of,respectively,then is a (∈,∈∨q)-fuzzy subgroup of.
Keywords:(&isin    &isin  &or  q)-fuzzy subgroup  (&isin    &isin  &or  q)-fuzzy normal subgroup  (&isin    &isin  &or  q)-fuzzy normalizer  (&isin    &isin  &or  q)-fuzzy centralizer  (&isin    &isin  &or  q)-fuzzy quotient subgroup
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