| 具有中心幂等元的L-弱正则半群 |
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| 引用本文： | 袁莹,任学明,宫春梅. 具有中心幂等元的L-弱正则半群[J]. 数学杂志, 2012, 32(1): 135-139 |
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| 作者姓名： | 袁莹 任学明 宫春梅 |
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| 作者单位： | 西安建筑科技大学数学系,陕西西安,710055 |
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| 基金项目： | 国家自然科学基金，西安建筑科技大学青年科技基金 |
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| 摘 要： | 本文定义了具有中心幂等元的(L)-弱正则半群,研究了这类半群的代数结构.利用半群上的右同余(L)+和左同余R+,证明了半群S是一个具有中心幂等元的(L)-弱正则半群,当且仅当S是H-左可消幺半群的强半格.这推广了Clifford半群的相应结果.
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| 关 键 词： | (L)-弱正则半群 中心幂等元 H-左可消幺半群 |
ON WEAKLY(L)-REGULAR SEMIGROUPS WITH CENTRAL IDEMPOTENTS |
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| YUAN Ying , REN Xue-ming , GONG Chun-mei. ON WEAKLY(L)-REGULAR SEMIGROUPS WITH CENTRAL IDEMPOTENTS[J]. Journal of Mathematics, 2012, 32(1): 135-139 |
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| Authors: | YUAN Ying REN Xue-ming GONG Chun-mei |
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| Affiliation: | (Dept.of Math.,Xi’an University of Architecture and Technology,Xi’an 710055,China) |
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| Abstract: | Weakly L-regular semigroups with central idempotents are introduced and their algebraic structures are studied in this paper.By using a right congruence L+ and a left congruence R+ on a semigroup S,respectively,we show that a semigroup S is a weakly L-regular semigroup with central idempotents if and only if S is a strong semilattice of H-left cancellative monoids,which generalizes the corresponding results of Clifford semigroups in the class of regular semigroups. |
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| Keywords: | weakly L-regular semigroups central idempotents H-left cancellative monoids |
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