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Several studies over the structure of semigroup theory
Author: GaoFei
Tutor: XieXiangYun
School: Wuyi University
Course: Applied Mathematics
Keywords: Rees hypercongruences Fuzzy Rees hypercongruences fuzzy hyperideal hypersemigroups hypersemigroup regular hypersemigroup intra-regular hypersemigroup fuzzy (generalized)hyper bi-ideal fuzzy hyper quasi-ideal
CLC: O152.7
Type: Master's thesis
Year: 2011
Downloads: 22
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Abstract
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Fuzzy hypercongruence relations and fuzzy hyperideals play an important role in the pro-cess of hyper algebraic structures. Most of time, using these fuzzy hypercongruence relations and fuzzy hyperideals, we obtained the structures and properties of homomorphic image of the hyper algebraic structures.In this paper, Rees hypercongruences and fuzzy Rees hypercongruences on hypersemi-groups are studied. Moreover, we generalize a homomorphism theorem of Davvaz in [5]. At the same time we introduce the concept of the fuzzy generalized hyper bi-ideals of a hypersemi-group, and regular hypersemigroups are characterized by means of fuzzy left hyperideals, fuzzy right hyperideals and fuzzy (generalized) hyper bi-ideals. Finally, we give two main theorems which characterize the regular hypersemigroups and intra-regular hypersemigroups in terms of fuzzy left hyperideals, fuzzy right hyperideals, fuzzy hyper bi-ideals, fuzzy hyper quasi-ideals. The paper shows that one can pass from results in terms of fuzzy subsets in semigroups or ordered semigroups to hypersemigroups.In Chapter One, we introduce the backgroud of this thesis and some basic concepts.In Chapter two, Using the concept of Rees congruences on semigroups and fuzzy sets presented by Zadeh, we have investigated the Rees hypercongruences and fuzzy Rees hyper-congruences on a hypersemigroups, we also introduce fuzzy Rees weak hypercongruences hy-persemigroup and give characterizations of hypercongruences on FRW H-semigroups.In Chapter three, we introduce the concept of the fuzzy generalized hyper bi-ideals of a hypersemigroup, and regular hypersemigroups are characterized by means of fuzzy left hyper-ideals, fuzzy right hyperideals and fuzzy (generalized) hyper bi-ideals. Finally, we give two main theorems which characterize the regular hypersemigroups and intra-regular hypersemi-groups in terms of fuzzy left hyperideals, fuzzy right hyperideals, fuzzy hyper bi-ideals, fuzzy hyper quasi-ideals.
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