| 序半群半直积的I-正则性 |
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| 引用本文： | 石小平 许永平 赵华. 序半群半直积的I-正则性[J]. 南京林业大学学报(自然科学版), 2004, 28(4): 34-38 |
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| 作者姓名： | 石小平 许永平 赵华 |
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| 作者单位： | [1]南京林业大学，江苏南京210037 [2]中国人民解放军理工大学，江苏南京210101 [3]南京大学，江苏南京210093 |
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| 基金项目： | 南京林业大学校基金资助项目 ( 0 63 0 70 72 0 ) |
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| 摘 要： | 半群的半直积与圈积是构造和研究半群的重要方法之一。目前对一般半群(不带序的半群)的半直积及圈积的研究已有许多结论，但是对序半群半直积与圈积的研究很少。I-正则半群和I-逆正则半群是正则半群和逆正则半群在序半群中的推广，它们是两类重要的序半群。笔引入了序半群的半直积的概念，给出了两个序半群的半直积是I-正则和I-逆正则半群的充要条件，将其应用到圈积中，得到圈积是I-正则和I-逆正则半群的充要条件。
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| 关 键 词： | I-正则半群 I-逆正则半群 半直积 圈积 |
I-regularirty of Semidirect Product of Ordered Semigroups |
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| SHI Xiao-ping. I-regularirty of Semidirect Product of Ordered Semigroups[J]. Journal of Nanjing Forestry University(Natural Sciences ), 2004, 28(4): 34-38 |
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| Authors: | SHI Xiao-ping |
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| Affiliation: | SHI Xiao-ping~ |
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| Abstract: | It is an important method to construct and study semigroups by the semidirect product and wreath product of two semigroups.At present,there are many reports in the semidirect product and wreath product of semigroups(without ordered relation),but there are few references in the semidirect product and wreath product of ordered semigroups.I-regular and I-inverse semigroups are two important classes ordered semigroups as a generalization of regular and inverse semigroups.In this paper,the semidirect product of two pomonoids are introduced,and necessary and sufficient condition are determined for the semidirect product of two ordered monoids to be I-regular and I-inverse semigroup,as an application in wreath product,main theorems in reference and are obtained. |
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| Keywords: | I-regular semigroup I-inverse semigroup Semidirect product Wreath product |
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