密码rpp半群上的同余
Congruences on Normal Cryptic rpp Semigroups
DOI: 10.12677/PM.2019.95074, PDF,    国家自然科学基金支持
作者: 郭文娟:江西师范大学教育学院,江西 南昌;郭小江:江西师范大学数学与信息科学学院,江西 南昌
关键词: rpp半群密码rpp半群酉同余rpp Semigroup Cryptic rpp Semigroup Unary Congruence Trace
摘要: 本文的主要目的是研究密码rpp半群的同余,得到了这类半群上的L*-酉同余迹的一些性质。另外,也考虑了一些特殊L*-酉同余。
Abstract: The aim of this note is to study congruences on cryptic rpp semigroups. Some properties of traces of L*-unary congruences on this class of semigroups are obtained. Also, some special cases are considered.
文章引用:郭文娟, 郭小江. 密码rpp半群上的同余[J]. 理论数学, 2019, 9(5): 557-562. https://doi.org/10.12677/PM.2019.95074

参考文献

[1] Guo, Y.Q., Shum, K.P. and Zhu, P.Y. (1995) The Structure of Left C-rpp Semigroups. Semigroup Forum, 50, 9-23.
[Google Scholar] [CrossRef
[2] Guo, J.Y., Guo, X.J. and Ding, J.Y. (2015) Completely J(ℓ)-Simple Semigroups. Advances in Mathematics (China), 44, 710-718.
[3] Guo, J.Y., Guo, X.J. and Ding, J.Y. (2015) Free Completely J(ℓ)-Simple Semi-groups. Acta Mathematica Sinica, English Series, 31, 1086-1096.
[Google Scholar] [CrossRef
[4] Guo, X.J. (2000) The Structure of NBe-rpp Semigroups. Northeastern Mathematical Journal, 4, 398-404.
[5] Guo, X.J., Guo, Y.Q. and Shum, K.P. (2008) Rees Matrix Theorem for D(ℓ)-Simple Strongly Rpp Semigroups. Asian-European Journal of Mathematics, 1, 215-223.
[Google Scholar] [CrossRef
[6] Guo, X.J., Guo, Y.Q. and Shum, K.P. (2010) Super Rpp Semigroups. Indian Journal of Pure and Applied Mathematics, 41, 505-533.
[Google Scholar] [CrossRef
[7] 郭小江. 满足置换恒等式的强rpp半群的结构[J]. 科学通报, 1996, 41(18): 1647-1650.
[8] 郭俊颖, 郭小江, 叶火平. 正规密码rpp半群上的同余[J]. 江西师范大学学报: 自然科学版, 2017, 41(4): 360-366.
[9] Guo, X.J., Jun, Y.P. and Zhao, M. (2010) Pseudo-C-Rpp Semi-groups. Acta Mathematica Sinica, 26, 629-646.
[Google Scholar] [CrossRef
[10] Guo, X.J., Shum, K.P. and Guo, Y.Q. (2001) Perfect Rpp Semigroups. Com-munications in Algebra, 29, 2447-2459.
[Google Scholar] [CrossRef
[11] 郭小江, 吴爱军. 关于左C-Rpp半群的一点注记[J]. 江西师范大学学报: 自然科学版, 2005, 29(4): 283-286.
[12] Guo, X.J. and Yang, Y.P. (2013) Cryptic Rpp Semigroups. Advances in Mathematics (China), 42, 465-474.
[13] Guo, X.J., Zhao, M. and Shum, K.P. (2008) Wreath Product Structure of Left C-Rpp Semigroups. Algebra Collo-quium, 15, 101-108.
[Google Scholar] [CrossRef
[14] 郭聿琦, 岑嘉评, 朱聘瑜. 左C-rpp半群的结构[J]. 科学通报, 1992(4): 292-294.
[15] 郭聿琦. 左C-rpp半群的右对偶[J]. 科学通报, 1997(19): 1599-1603.
[16] He, Y., Guo, Y.Q. and Shum, K.P. (2004) The Construction of Orthodox Super Rpp Semigroups. Science in China, 17, 552-565.
[Google Scholar] [CrossRef
[17] Shum, K.P., Guo, X.J. and Ren, X.M. (2000) ${(\ell)}$-Green’s Relations and Perfect Rpp Semigroups. In: Sunada, T., Polly, W.S. and Yang, L., Eds., Proceedings of the 3th Asian Mathematical Conference, 604-613.
[18] Shum, K.P. and Ren, X.M. (2004) The Structure of Right C-Rpp Semigroups. Semigroup Forum, 68, 280-292.
[Google Scholar] [CrossRef
[19] Wang, J.Q., Guo, X.J. and Qiu, X.W. (2014) Regular OS-Rpp Semigroups. Bulletin of the Malaysian Mathematical Sciences Society, 37, 597-610.
[20] Yang, Y.P. and Guo, X.J. (2009) Orthocryptic Rpp Semigroups. International Mathematical Forum, 42, 2065-2074.
[21] 叶火平, 郭俊颖, 郭小江. 超rpp半群的核心[J]. 理论数学, 2016(6): 172-176.
[22] 王莹, 郭俊颖, 吴灏驰, 郭小江. 密码rpp半群的若干特征[J]. 江西师范大学学报: 自然科学版, 2019, 43(1): 22-27.
[23] Petrich, M. and Reilly, N.R. (1999) Completely Regular Semigroups. John Wiley & Sons, New York.
[24] Howie, J.M. (1976) An Introduction to Semigroup Theory. Academic Press, London.