Abstract
A semigroup is called completely J (ℓ) -simple if it is isomorphic to some Rees matrix semigroup over a left cancellative monoid and each entry of whose sandwich matrix is in the group of units of the left cancellative monoid. It is proved that completely J (ℓ)-simple semigroups form a quasivarity. Moreover, the construction of free completely J (ℓ)-simple semigroups is given. It is found that a free completely J (ℓ)-simple semigroup is just a free completely J*-simple semigroup and also a full subsemigroup of some completely simple semigroups.
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Burries, S., Sankappanavar, H. P.: A Course in Universsal Algebra, World Scientific Publishing Co. Pte. Ltd., Singapore, 1981
Fountain, J. B.: Abundant semigroups. Proc. London Math. Soc., 44(3), 103–129 (1982)
Guo, X. J., Guo, Y. Q., Shum, K. P.: Super rpp semigroups. Indian J. Pure Appl. Math., 41, 505–533 (2010)
Guo, X. J., Guo, Y. Q., Shum, K. P.: Rees matrix theorem for D (ℓ)-simple strongly rpp semigroups. Asian-European J. Math., 1, 215–223 (2008)
Guo, X. J., Jun, Y. B., Zhao, M.: Psuedo-C-rpp semigroups. Acta Math. Sin., Engl. Series, 26, 629–646 (2010)
Guo, X. J., Ren, C. C., Shum, K. P.: Dual wreath product structure of right C-rpp semigroups. Algebra Colloq., 14, 285–294 (2007)
Guo, X. J., Shum, K. P., Guo, Y. Q.: Perfect rpp semigroups. Comm. Algebra, 29, 2447–2460 (2001)
Guo, X. J., Zhao, M., Shum, K. P.: Wreath product structure of left C-rpp semigroups. Algebra Colloq., 15, 101–108 (2008)
Guo, Y. Q.: On the dual of left C-rpp semigroups. Chinese Sci. Bull., 24, 1599–1603 (1997)
Guo, Y. Q., Shum, K. P., Zhu, P. Y.: The structure of left C-rpp semigroups. Semigroup Forum, 50, 9–23 (1995)
Howie, J. M.: An Introduction to Semigroup Theory, Academic Press, London, 1976
Lawson, M. V.: Abundant Rees matrix semigroups. J. Austral. Math. Soc. (Ser. A), 42, 132–142 (1987)
Petrich, M.: Lectores in Semigroups, Akademic-Verlag, Berlin, 1977
Petrich, M., Reilly, N. R.: Completely Regular Semigroups, John Wiley & Sons, New York, 1999
Shum, K. P., Guo, X. J., Ren, X. M.: (ℓ)-Green’s relations and perfect rpp semigroups. In: Proceeding of the 3th Asian Mathematical Conference (ed: T. Sunada, W.S. Polly and L. Yang), 2000, 604–613
Shum, K. P., Ren, X. M.: The structure of right C-rpp semigroups. Semigroup Forum, 68, 280–292 (2004)
Wang, J. Q., Guo, X. J., Qiu, X. W.: Regular OS-rpp semigroups. Bull. Malays. Math. Sci. Soc. (2), 37, 597–610 (2014)
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Supported by National Natural Science Foundation of China (Grant No. 11361027); the Natural Science Foundation of Jiangxi Province and the Science Foundation of the Education Department of Jiangxi Province, China
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Guo, J.Y., Guo, X.J. & Ding, J.Y. Free completely J (ℓ)-simple Semigroups. Acta. Math. Sin.-English Ser. 31, 1086–1096 (2015). https://doi.org/10.1007/s10114-015-4117-8
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DOI: https://doi.org/10.1007/s10114-015-4117-8