Fuzzy Good Congruences on Left Semiperfect Abundant Semigroups |
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| Authors: | Chunhua Li Ergen Liu |
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| Institution: | 1. School of Mathematics , South China Normal University , Guangzhou , Guangdong , China;2. School of Basic Science , East China Jiaotong University , Nanchang , Jiangxi , China chunhuali66@163.com;4. School of Basic Science , East China Jiaotong University , Nanchang , Jiangxi , China |
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| Abstract: | Motivated by studying fuzzy congruences in groups, semigroups, and ordered semigroups, and as a continuation of N. Kuroki and Y. Tan's works in regular semigroups in terms of fuzzy subsets, in this article we introduce the notions of a fuzzy good congruence relation, a fuzzy cancellative congruence relation on abundant semigroups, and give some properties, and characterizations of fuzzy good congruences on such semigroups. Furthermore, we characterize fuzzy good congruences of left semiperfect abundant semigroups, and get sufficient and necessary conditions for an abundant semigroup to be left semiperfect. |
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| Keywords: | Abundant semigroup Fuzzy congruence Fuzzy good (cancellative) congruence Left semiperfect abundant semigroup |
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