| On Weak Regular ^＊-semigroups |
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| 作者姓名： | YongHuaLI HalBinKAN BingJunYU |
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| 作者单位： | [1]DepartmentofMathematics,SouthChinaNormalUniversity,Guangzhou510631,P.R.China [2]DepartmentofComputer,FudanUniversity,Shanghai200433,P.R.China [3]DepartmentofMathematics,SichuanNormalUniversity,Chengdu610066,P.R.China |
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| 摘 要： | In this paper, a special kind of partial algebras called projective partial groupoids is defined.It is proved that the inverse image of all projections of a fundamental weak regular ^*-semigroup under the homomorphism induced by the maximum idempotent-separating congruence of a weak regular ^*-semigroup has a projective partial groupoid structure. Moreover, a weak regular ^*-product which connects a fundamental weak regular ^*-semigroup with corresponding projective partial groupoid is defined and characterized. It is finally proved that every weak regular ^*-product is in fact a weak regular ^*-semigroup and any weak regular ^*-semigroup is constructed in this way.
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| 关 键 词： | 弱＊-半群 一元算子 ＊-同态 群论 部分投影 |
| 收稿时间： | 7 June 2000 |
On Weak Regular *-semigroups |
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| YongHuaLI HalBinKAN BingJunYU.On Weak Regular *-semigroups[J].Acta Mathematica Sinica,2004,20(3):569-576. |
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| Authors: | Email author" target="_blank">Yong?Hua?LiEmail author Hai?Bin?Kan Bing?Jun?Yu |
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| Institution: | (1) Department of Mathematics, South China Normal University, Guangzhou, 510631, P. R. China;(2) Department of Computer, Fudan University, Shanghai, 200433, P. R. China;(3) Department of Mathematics, Sichuan Normal University, Chengdu, 610066, P. R. China |
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| Abstract: | Abstract
In this paper, a special kind of partial algebras called projective partial groupoids is defined. It is proved that the inverse image of all projections of a fundamental weak regular *-semigroup under the homomorphism
induced by the maximum idempotent-separating congruence of a weak regular *-semigroup has a projective partial groupoid structure.
Moreover, a weak regular *-product which connects a fundamental weak regular *-semigroup with corresponding projective partial groupoid is defined and characterized.
It is finally proved that every weak regular *-product is in fact a weak regular *-semigroup and any weak regular *-semigroup
is constructed in this way.
Subject supported by NNSF of China (60002007) and NSF of Guangdong China (011438) |
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| Keywords: | Weak regular *-semigroup Projective partial groupoid Weak regular *-product |
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