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Wreath Product Structure of Left C-rpp Semigroups

2008; World Scientific; Volume: 15; Issue: 01 Linguagem: Inglês

10.1142/s1005386708000102

1005-3867

Xiaojiang Guo, Ming Hao Zhao, K. P. Shum,

Advanced Algebra and Logic

Algebra ColloquiumVol. 15, No. 01, pp. 101-108 (2008) No AccessWreath Product Structure of Left C-rpp SemigroupsXiaojiang Guo, Ming Zhao, and K. P. ShumXiaojiang GuoCollege of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi 330027, China, Ming ZhaoCollege of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi 330027, China, and K. P. ShumDepartment of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong, Chinahttps://doi.org/10.1142/S1005386708000102Cited by:5 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail AbstractThe concept of wreath product of semigroups was first introduced by Neumann in 1960, and later on, this concept was used by Preston to investigate the structure of some inverse semigroups. In this paper, we modify the wreath product given by Neumann and Preston to study the structure of some generalized Clifford semigroups. In particular, we prove that a semigroup is a left C-rpp semigroup if and only if it is the wreath product of a left regular band and a C-rpp semigroup. Our result provides a new insight to the structure of left C-rpp semigroups.The first and second authors are supported by the Natural Science Foundation of Jiangxi Province and the Science Foundation of Education Department of Jiangxi Province, China, and the third author is partially supported by a UGC (HK) grant #2160210/04-05.Keywords:left C-rpp semigroupleft regular bandleft cancellative monoidwreath productAMSC: 20M10 References J. B. Fountain, Semigroup Forum 13, 229 (1977), DOI: 10.1007/BF02194941. Crossref, Google ScholarJ. B. Fountain, Proc. London Math. Soc. 44, 103 (1982). ISI, Google ScholarX. J. Guo, Chinese Science Bulletin 41, 1647 (1996). Crossref, Google ScholarX. J. Guo, Northeastern Math. J. 16, 398 (2000). Google ScholarX. J. Guo and Y. Q. Guo, Science in China 29, 1002 (2000). Google ScholarX. J. Guo, Y. Q. Guo and K. P. Shum, Semigroups, eds. K. P. Shumet al. (Springer-Verlag, Singapore, 1998) pp. 157–166. Google ScholarX. J. Guo, Y. Q. Guo and K. P. Shum, Comm. Algebra 32, 2061 (2004), DOI: 10.1081/AGB-120037207. Crossref, ISI, Google ScholarX. J. Guo and K. P. Shum, Inter. Math. J. 5, 705 (2004). ISI, Google ScholarX. J. Guo, K. P. Shum and Y. Q. Guo, Comm. Algebra 29(6), 2447 (2001), DOI: 10.1081/AGB-100002109. Crossref, ISI, Google ScholarX. J. Guo and A. J. Wu, J. Jiangxi Normal Univ. 29, 283 (2005). Google ScholarY. Q. Guo, Chinese Science Bulletin 42, 1599 (1997), DOI: 10.1007/BF02882566. Crossref, ISI, Google ScholarY. Q. Guo, K. P. Shum and P. Y. Zhu, Semigroup Forum 50, 9 (1995). ISI, Google ScholarG. Li and K. P. Shum, J. Appl. Algebra Discrete Struct. 4(1), 1 (2006). ISI, Google ScholarB. H. Neumann, J. London Math. Soc. 35, 184 (1960). Google ScholarW. R. Nico, J. Algebra 80, 29 (1973), DOI: 10.1016/0021-8693(83)90015-7. Crossref, ISI, Google ScholarG. B. Preston, Ordered Structures and Algebra of Computer Languages (World Scientific, Singapore, 1993) pp. 161–169. Google Scholar FiguresReferencesRelatedDetailsCited By 5Congruences on Normal Cryptic rpp Semigroups文娟 郭1 Jan 2019 | Pure Mathematics, Vol. 09, No. 05Free completely J (ℓ)-simple SemigroupsJun Ying Guo, Xiao Jiang Guo and Juan Ying Ding15 June 2015 | Acta Mathematica Sinica, English Series, Vol. 31, No. 7A New Construction for Inverse Semigroups姗姗 刘1 Jan 2015 | Pure Mathematics, Vol. 05, No. 02Orthodox Super rpp Semigroups瑕 吴1 Jan 2013 | Pure Mathematics, Vol. 03, No. 02Pseudo-C-rpp semigroupsXiao Jiang Guo, Young Bae Jun and Ming Zhao15 February 2010 | Acta Mathematica Sinica, English Series, Vol. 26, No. 4 Recommended Vol. 15, No. 01 Metrics History Received 22 November 2005 Revised 20 January 2006 Keywordsleft C-rpp semigroupleft regular bandleft cancellative monoidwreath productPDF download