半群的R-模糊理想  

R-Fuzzy Ideals of Semigroups

作　　者：朱晓英[1] 廖祖华[1] 郝翠芸[1] 田超超[1] 

机构地区：[1]江南大学理学院,江苏无锡214122

出　　处：《江南大学学报（自然科学版）》2011年第5期612-616,共5页Joural of Jiangnan University (Natural Science Edition)　

基　　金：国家自然科学基金项目(11001109);江苏省教育科学"十一五"规划基金项目(D/2006/01/171);江苏省教育厅基金项目(2009-598);江南大学大学生创新训练计划项目(2010-596)

摘　　要：R-蕴涵算子与半群的模糊理想相结合引入半群的R-模糊理想的定义,得到了当R(x,y)对变量x递减时,两个半群的R-模糊理想的交仍是半群的R-模糊理想,当R(xy,)对变量x递增时,两个半群的R-模糊理想的并仍是半群的R-模糊理想的相关定理及推论。基于半群同态的定义,研究了R-模糊理想的满同态像及同态原像的相关性质,推出半群的R-模糊理想的满同态像及同态原像仍是半群的R-模糊理想;最后给出半群的R-模糊理想在8个蕴涵算子上的特征刻画。The definition of R-fuzzy ideals of semigroups is introduced by combining R-implication operations and fuzzy ideals of semigroups.And we obtain the related theories and deductions that the intersection of two R-fuzzy ideals of semigroups is still a R-fuzzy ideal of semigroups when R（x,y） is decreasing on the variable x and the union of two R-fuzzy ideals of semigroups is still a R-fuzzy ideal of semigroups when R（x,y） is increasing on the variable x.Based on the definition of semigroup homomorphism,we study the related properties of full homomorphic images and homomorphic preimages of R-fuzzy ideals of semigroups,deducing that the full homomorphic image or homomorphic preimage of a R-fuzzy ideal of semigroups is still a R-fuzzy ideal of semigroups.Finally,the feature descriptions of R-fuzzy ideals of semigroups on eight implication operations are given.

关 键 词：半群的R-模糊理想 R-蕴涵算子 半群同态 满同态像 同态原像 

分 类 号：O175.1[理学—数学]