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| D-半群上的拓扑 | |
| 引用本文： | 潘芳芳,曹文营,王顺钦.D-半群上的拓扑[J].南阳师范学院学报,2014(9):1-3. |
| 作者姓名： | 潘芳芳 曹文营 王顺钦 |
| 作者单位： | 1. 西安邮电大学理学院,陕西西安,710121 2. 驻马店市第二初级中学,河南驻马店,463000 3. 南阳师范学院数学与统计学院,河南南阳,473061 |
| 基金项目： | 国家自然科学基金资助项目(11001158)；西安邮电大学青年教师科研基金项目(ZL2014-38)；河南省基础与前沿技术研究计划项目 |
| 摘 要： | 研究D-半群的结构性质.借助于Rees序,建立了D-半群范畴和序半群范畴之间的函子,并证明了幂等可换半群范畴ICSGr是D-半群范畴DSGr的余反射子范畴,同时,也研究了D-半群S上的右理想拓扑τS,证明了(S,τS)是T0-空间当且仅当S是幂等可换的半群,并且d=idS. |
| 关 键 词： | D-半群 Rees序 序半群 T0-空间 范畴 |
Topology on D-semigroups |
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| PAN Fang-fang,CAO Wen-ying,WANG Shun-qin.Topology on D-semigroups[J].Journal of Nanyang Teachers College,2014(9):1-3. | |
| Authors: | PAN Fang-fang CAO Wen-ying WANG Shun-qin |
| Institution: | PAN Fang-fang, CAO Wen-ying, WANG Shun-qin (1. Department of Mathematics, Xi＇an University of Posts and Telecommunication, Xi＇an 710121, China; 2. The Second Junior Middle School of Zhumadian City, Zhumadian 463000, China; 3. School of Mathematics and Statistics, Nanyang Normal University, Nanyang 473061, China) |
| Abstract: | The main purpose of this paper is to investigate the structure of D-semigroups, where D-semigroups may be viewed as generalizations of inverse semigroups. In terms of Rees order, we build a functor from the cate- gory of D-semigroups to the category of ordered semigroups, and prove that the category ICSGr of idempotent and commutative semigroups is a reflective subeategory of the category DSGr of D-semigroups. Furthermore, we also prove that for the right ideal topology τs on a D-semigroup S, （S, τs） is a T0-space if and only if S is an idempotent commutative semigroup and d = ids. |
| Keywords: | D-semigroup Rees order ordered semigroup T0-space category |
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