Abstract
The aim of this paper is to study a class of right pp semigroups, so-called pseudo-C-rpp semigroups. After obtaining some characterizations of pseudo-C-rpp semigroups, we establish a construction of such semigroups in terms of left normal bands and right C-rpp semigroups. In particular, a special case is considered.
Similar content being viewed by others
References
Fountain, J. B.: Abundant semigroups. Proc. London Math. Soc., 44, 103–129 (1982)
Fountain, J. B.: Right pp momids with central idempotents. Semigroup Forum, 13, 9–23 (1977)
Guo, X. J., Guo, Y. Q., Shum, K. P.: Left abundant semigroups. Communications in Algebra, 32, 2061–2085 (2004)
Guo, Y. Q., Shum, K. P., Zhu, P. Y.: The structure of left C-rpp semigroups. Semigroup Forum, 50, 9–23 (1995)
Guo, X. J.: The structure of PI-strongly rpp semigroups. Chinese Science Bulletin, 41, 1647–1650 (1996)
Guo, X. J.: The structure of Nbe-rpp semigroups. Northeastern Math. J., 16, 398–404 (2000)
Guo, X. J., Guo, Y. Q.: The translational hull on a strongly right type-A semigroup. Sci. China, Ser. A, 29, 1002–1008 (2000)
Guo, X. J., Guo, Y. Q., Shum, K. P.: Semispined product structure of left C-a semigroups. In: Semigroups (ed: K.P. Shum, Y.Q. Guo et al.), Springer-Verlag, Singapore, 157–166 (1998)
Guo, X. J., Ren, C. C., Shum, K. P.: Dual wreath product structure of right C-rpp semigroups. Algebra Colloquium, 14, 285–294 (2007)
Guo, X. J., Shum, K. P.: On left cyber groups. Inter. Math. J., 5, 705–717 (2004)
Guo, X. J., Shum, K. P., Guo, Y. Q.: Perfect rpp semigroups. Communications in Algebra, 29, 2447–2460 (2001)
Guo, Y. Q.: On the dual of left C-rpp semigroups. Chinese Science Bulletin, 42, 1599–1603 (1997)
Guo, Y. Q., Ren, X. M., Shum, K. P.: Another structure of left C-semigroups. Advances in Mathematics (China), 24(1), 39–43 (1995)
Shum, K. P., Guo, X. J., Ren, X. M.: (ℓ)-Green’s relations and perfect rpp semigroups. In: Proceedings of the 3th Asian Mathematical Conference 2000 (ed: T. Sunada, W.S. Polly and L. Yang), 604–613
Shum, K. P., Ren, X. M.: The structure of right C-rpp semigroups. Semigroup Forum, 68, 280–292 (2004)
Guo, X. J., Wu, A. J.: A note on left C-rpp semigroups. J. Jiangxi Normal Univ. (Natural Sci.), 29, 283–286 (2005)
Guo, X. J., Zhao, M., Shum, K. P.: Wreath product structure of left C-rpp semigroups. Algebra Colloquium, 15, 101–108 (2008)
Howie, J. M.: An Introduction to Semigroup Theory, Academic Press, London, 1976
Petrich, M.: Lecture in Semigroups, Akademic Verlag, Berlin, 1977
Guo, Y. Q.: Weakly left C-semigroups. Chinese Science Bull., 41, 462–467 (1996)
Guo, Y. Q., Shum, K. P., Zhu, P. Y.: On quasi-C-semigroups and some special subclasses. Algebra Colloquium, 6, 105–120 (1999)
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by the NSF of Jiangxi Province, the SF of Education Department of Jiangxi Province and the SF of Jiangxi Normal University
Rights and permissions
About this article
Cite this article
Guo, X.J., Jun, Y.B. & Zhao, M. Pseudo-C-rpp semigroups. Acta. Math. Sin.-English Ser. 26, 629–646 (2010). https://doi.org/10.1007/s10114-010-8030-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10114-010-8030-x
Keywords
- right pp semigroup
- left normal band
- strongly rpp semigroup
- right quasi-normal band
- right regular band
- left cancellative monoid