左#-富足半群上的偏序
The Partial Order on Left #-Abundant Semigroups
DOI: 10.12677/pm.2025.1512303, PDF,    科研立项经费支持
作者: 刘海军, 宋 杰*：韶关学院数学与统计学院，广东 韶关
关键词: Green#-关系；左#-富足半群；偏序；Green#-Relations； Left#-Abundant Semigroup； Partial Order
摘要: 本文主要研究左#-富足半群上的偏序≤。我们给出这种偏序的若干刻画和性质，并证明了左#-富足半群上偏序关于乘法的(左，右)相容性定理，这些结果推广了正则半群和富足半群上自然偏序的相关理论。
Abstract: The aim of this paper is to study the partial order ≤ on left#-abundant semigroups. We obtain several descriptions and properties for this kind of partial order and show the (left, right) compatible theorem with respect to the multiplication on left#-abundant semigroups. These results enrich the related theory with respect to the natural partial orders on regular semigroups and abundant semigroups.
文章引用：刘海军, 宋杰. 左#-富足半群上的偏序[J]. 理论数学, 2025, 15(12): 148-153. https://doi.org/10.12677/pm.2025.1512303

参考文献

[1] Nambooripad, K.S.S. (1980) The Natural Partial Order on a Regular Semigroup. Proceedings of the Edinburgh Mathematical Society, 23, 249-260. [Google Scholar] [CrossRef] 
[2] Lawson, M.V. (1987) The Natural Partial Order on an Abundant Semigroup. Proceedings of the Edinburgh Mathematical Society, 30, 169-186. [Google Scholar] [CrossRef] 
[3] Guo, X.J. and Luo, Y.L. (2005) The Natural Orders on Abundant Semigroups. Advances in mathematics, 34, 297-308.
[4] Guo, X.J. and Shum, K.P. (2006) The Lawson Partial Order on RPP Semigroups. International Journal of Pure and Applied Mathematics, 29, 415-423.
[5] Liu, H.J., Guo, X.J. and Qiu, S.M. (2009) The Natural Partial Orders on WPP Semigroups. International Mathematical Forum, 4, 1563-1572.
[6] Liu, H.J. and Guo, X.J. (2012) The Lawson Partial Order on WRPP Semigroups. Chinese Quarterly Journal of Mathematics, 27, 139-144.
[7] 李春华, 黄华伟, 朱咏前, 李小平. 富足半群上的自然偏序[J]. 江西师范大学学报(自然科学版), 2004(1): 24-26.
[8] Fountain, J. (1982) Abundant Semigroups. Proceedings of the London Mathematical Society, 3, 103-129. [Google Scholar] [CrossRef] 
[9] Fountain, J. (1979) Adequate Semigroups. Proceedings of the Edinburgh Mathematical Society, 22, 113-125. [Google Scholar] [CrossRef] 
[10] Howie, J.M. (1995) Fundamentals of Semigroup Theory. Clarendon Press.
[11] Xiangdong, T. (1997) On a Theorem of C—WRPP Semigroups. Communications in Algebra, 25, 1499-1504. [Google Scholar] [CrossRef] 
[12] Kong, X. and Shum, K.P. (2009) Green ♯-Relations and Normal-Cryptogroups. Asian-European Journal of Mathematics, 2, 637-648. [Google Scholar] [CrossRef] 
[13] Du, L., Guo, Y. and Shum, K. (2010) Green’s Relations and Their Generalizations on Semigroups. Discussiones Mathematicae—General Algebra and Applications, 30, 71-89. [Google Scholar] [CrossRef] 
[14] Du, L. and Shum, K.P. (2003) On Left C-WRPP Semigroups. Semigroup Forum, 67, 373-387. [Google Scholar] [CrossRef] 
[15] Lawson, M.V. (1986) The Structure of Type A Semigroups. The Quarterly Journal of Mathematics, 37, 279-298. [Google Scholar] [CrossRef] 

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