纯正超rpp半群
Orthodox Super rpp Semigroups
DOI: 10.12677/PM.2013.32018, PDF,  被引量 下载: 2,960  浏览: 6,416  国家自然科学基金支持
作者: 吴 瑕*, 郭小江, 邱小伟*:江西师范大学数学与信息科学学院
关键词: 超rpp半群OS-rpp半群C-rpp半群同余 (l)-主因子 Super rpp Semigroup; OS-rpp Semigroup; C-rpp Semigroup; (l)-Principal Factor
摘要: 本文研究纯正超rpp半群,得到了这类半群的若干新性质和特征,并且给出了纯正超rpp半群上的幂等元分离同余的刻画。此外,还给出了左C-rpp半群和右C-rpp半群的等价刻画。
Abstract: The aim of this paper is to study orthodox super rpp semigroups. Some new properties and characterizations of such semigroups are obtained. Also, idempotent-separating congruencies on orthodox super rpp semigroups are described. As an application, some properties of left C-rpp semigroups and right C-rpp semigroups are given.
文章引用:吴瑕, 郭小江, 邱小伟. 纯正超rpp半群[J]. 理论数学, 2013, 3(2): 112-119. http://dx.doi.org/10.12677/PM.2013.32018

参考文献

[1] J. B. Fountain. Right pp semigroup with central idempotents. Semigroup Forum, 1976, 13: 229-237.
[2] J. B. Fountain. Abundant semigroups. Proceedings of the London Mathematical Society, 1982, 44(3): 103-129.
[3] M. Petrich, N. R. Reilly. Completely regular semigroups. Hoboken: John Wiley&Sons, INC., 1999.
[4] Y. Q. Guo, K. P. Shum and P.Y. Zhu. The structure of left C-rpp semigroups. Semigroup Forum, 1995, 50(1): 9-23.
[5] Y. Q. Guo. The right dual of left C-rpp semigroups. Chinese Science Bulletin, 1997, 42: 1599-1603.
[6] K. P. Shum, X. M. Ren. The structure of right C-rpp semigroups. Semigroup Forum, 2004. 68(2): 280-292.
[7] X. J. Guo, C. C. Ren and K. P. Shum. Dual wreath product structure of right C-rpp semigroup. Algebra Colloquium, 2007, 2: 285-294.
[8] X. J. Guo, Y. B. Jun and M. Zhao. Pseudo-C-rpp semigroups. Acta Mathematica Sinica (English Series), 2010, 26(4): 629-646.
[9] X. J. Guo, K. P. Shum and Y. Q. Guo. Perfect rpp semigroups. Communications in Algebra, 2001, 29(6): 2447-2460.
[10] Y. He, Y. Q. Guo and K. P. Shum. The construction of orthodox super rpp semigroups. Science in China (Series A), 2004, 17: 552-565.
[11] J. B. Fountain. Adequate semigroups. Proceedings of the Edinburgh Mathematical Society, 1979, 22(2): 113-125.
[12] J. M. Howie. An introduction to semigroup theory. London: Academic Press, 1976.
[13] X. J. Guo, Y. Q. Guo and K. P. Shum. Rees matrix theorem for -simple strongly rpp semigroups. Asian-European Journal of Mathemat- ics, 2008, 1: 215-223.
[14] X. J. Guo, Y. Q. Guo and K. P. Shum. Super rpp semigroup. Indian Journal of Pure and Applied Mathematics, 2010, 41(4): 505-533.
[15] X. J. Guo, M. Zhao and K. P. Shum. Wreath product structure of left C-rpp semigroups. Algebra Colloquium, 2008, 15(1): 101-108.