| 无限集上严格保序变换半群的正则元及格林关系 |
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| 引用本文： | 许新斋,孟玲. 无限集上严格保序变换半群的正则元及格林关系[J]. 纯粹数学与应用数学, 2011, 27(3): 297-301 |
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| 作者姓名： | 许新斋 孟玲 |
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| 作者单位： | 1. 山东师范大学数学科学学院,山东济南,250014
2. 山东工业职业学院基础部,山东淄博,256414 |
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| 基金项目： | 山东省中青年科学家科研奖励基金(2008BS01016) |
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| 摘 要： | 设X是一个全序集,SOx是X上的严格保序变换半群.考虑X是一个全序无限集的情形.讨论了SOx中的正则元和SOx上的格林关系.证明了SOx中的元素α是正则的当且仅当α是双射.还证明了SOx的所有正则元形成SOx的一个极大子群.另外,给出了SOx上的格林关系L,R,D和H的刻划.SOx上格林关系的刻画对SOx的研究起重要作...
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| 关 键 词： | 严格保序变换半群 正则元 格林关系 |
Regular elements and Green's relations of strictly order-preserving transformation semigroup on an infinite set |
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| XU Xin-zhai,MENG Ling. Regular elements and Green's relations of strictly order-preserving transformation semigroup on an infinite set[J]. Pure and Applied Mathematics, 2011, 27(3): 297-301 |
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| Authors: | XU Xin-zhai MENG Ling |
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| Affiliation: | XU Xin-zhai 1,MENG Ling 2(1.School of Mathematical Science,Shandong Normal University,Ji'nan 250014,China,2.Basal Board,Shandong Industrially Vocational College,Zibo 256414,China) |
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| Abstract: | Let X be a totally ordered set and SOX the strictly order-preserving transformation semigroup on X.In this paper,the set X under consideration is a totally ordered infinite set.The regular elements in SOX and the green’s relations on SOX are discussed.It is shown that an element α in SOX is regular if and only if α is a bijection.It is also shown that all regular elements of SOX form a maximal subgroup of SOX.In addition,characterizations for the green’s relations L,R,D and H on SOX are given.The characterizations of green’s relations on SOX play an importent role for study of SOX. |
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| Keywords: | strictly order-preserving transformation semigroups regular elements Green's relations |
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