带正则*-断面的正则半群

王守峰, 张笛

数学学报 ›› 2011, Vol. 54 ›› Issue (4) : 591-600.

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中国科学院数学与系统科学研究院期刊网
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数学学报 ›› 2011, Vol. 54 ›› Issue (4) : 591-600. DOI: 10.12386/A2011sxxb0060
论文

带正则*-断面的正则半群

    王守峰1, 张笛2
作者信息 +

Regular Semigroups with Regular *-Transversals

    Shou Feng WANG1, Di ZHANG2
Author information +
文章历史 +

摘要

本文给出了带正则*-断面的正则半群的若干性质,获得了带拟理想正则*-断面的正则半群的一个构造方法.利用这一构造定理,考虑了这类半群上的同余.  

Abstract

In this paper, some remarkable properties of regular semigroups with a regular *-transversal are given. A construction method of a regular semigroup with a quasi-ideal regular *-transversal is obtained. Furthermore, congruences on this class of semigroups are also considered by applying our structure theorem.  

关键词

正则*-断面 / QR-系 / 同余

Key words

regular *-transversal / QR-system / congruence

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王守峰, 张笛. 带正则*-断面的正则半群. 数学学报, 2011, 54(4): 591-600 https://doi.org/10.12386/A2011sxxb0060
Shou Feng WANG, Di ZHANG. Regular Semigroups with Regular *-Transversals. Acta Mathematica Sinica, Chinese Series, 2011, 54(4): 591-600 https://doi.org/10.12386/A2011sxxb0060

参考文献

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[7] Ni X. F., Luo Y. F., Chao H. Z., Abundant semigroups with a quasi-ideal quasi-adequate transversal, Acta Mathematica Sinica, English Series, 2009, 25(10): 1653-1664.

[8] Li Y. H., On regular semigroups with a quasi-ideal regular *-transversal, Adv. Math. China 2003, 32(6): 727-738.

[9] Li Y. H., A class of regular semigroups with regular *-transversals, Semigroup Forum, 2002, 65(1): 43-57.

[10] Wang S. F., Liu Y., On P-regular semigroups having regular *-transversals, Semigroup Forum, 2008, 76(3): 561-575.

[11] Li Y. H., Wang S. F., Zhang R. H., Regular semigroups with regular *-transversals, J. Southwest China Normal University (Natural Science), 2006, 31(5): 52-56.

[12] Howie J. M., An Introduction to Semigroup Theory, London: Academic Press, 1976.

基金

国家自然科学基金(10871161);云南省教育厅项目(09Y0141),云南师范大学博士科研启动项目

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