| 模糊理想刻画的弱左正则幺半群 |
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| 引用本文： | 颜凤,谢祥云.模糊理想刻画的弱左正则幺半群[J].五邑大学学报(自然科学版),2008,22(4):24-27. |
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| 作者姓名： | 颜凤 谢祥云 |
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| 作者单位： | 1. 罗定职业技术学院,教育系,广东,罗定,527200
2. 五邑大学,数学物理系,广东,江门,529020 |
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| 摘 要： | 介绍弱左正则幺半群的概念，指出在可交换半群中，完全正则、弱左（右）正则和完全幂等是等价的．进一步地，通过模糊理想、模糊左理想和模糊右理想的性质刻画了弱左正则幺半群，给出了一个幺半群是弱左正则的等价条件．
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| 关 键 词： | 幺半群 弱左正则 左幂等 完全幂等 模糊幂等 |
Left Weakly Regular Monoids Characterized by Fuzzy Ideals |
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| YAN Feng,XIE Xiang-yun.Left Weakly Regular Monoids Characterized by Fuzzy Ideals[J].Journal of Wuyi University(Natural Science Edition),2008,22(4):24-27. |
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| Authors: | YAN Feng XIE Xiang-yun |
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| Institution: | YAN Feng, XIE Xiang-yun (1. Department of Education, Luoding Vocational ＆ Technological College, Luoding 527200, China; 2. Department of Mathematics and Physics, Wuyi University, Jiangmen 529020, China) |
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| Abstract: | In this paper, we introduce the notion of left weakly regular semigroup and show that in a commutative semigroup, the complete regularity, regularity, left （resp. right） regularity and full idempotent are equivalent. Furthermore, we characterize left weakly regular monoids by the properties of their fuzzy ideals, fuzzy left ideals and fuzzy right ideals, and give the equivalent conditions for a monoid to be left weakly regular. |
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| Keywords: | monoid left weakly regular left idempotent full idempotent fuzzy idempotent |
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