A structure theorem of left regular cyber-groups

Yıl 2017, Cilt: 46 Sayı: 6, 1093 - 1104, 01.12.2017

Ying Yuan Xueming Ren K. P. Shum

Öz

An abundant semigroup S is a superabundant semigroup if each $\mathcal{H}^*$-class of S contains an idempotent. We call a superabundant semigroup a left regular cyber-group if the set of its idempotents forms a left regular band. After the investigation of the properties of superabundant semigroups, we establish a structure theorem for the left regular cybergroups by using the newly defined left twist product of semigroups.

Anahtar Kelimeler

Completely regular semigroups, Superabundant semigroups, Left regular cyber-groups

Kaynakça

• G. L. Bailes, Right inverse semigroups, J. of Algebra 26 (1973), 492–507.
• A. El-Qallali and J. B. Fountain, Quasi-adequate semigroups, Proc. Roy. Soc. Edinburgh Sect. A, (1981), 91–99.
• J. B. Fountain, Adequate semigroups, Proc. Edinburgh Math. Soc. 22 (1979), 113–125.
• J. B. Fountain, Abundant semigroups, Proc. Lond. Math. Soc. 44 (1982), 103–129.
• X. J. Guo and K.P.Shum, On left cyber groups, Intern. Math. Journal 5(8) (2004), 705-717.
• J. M. Howie, An introduction to semigroup theory, Academic Press, London, 1976.
• J. M. Howie, Fundamentals of semigroup theory, Oxford University Press, New York, 1995.
• X.Z. Kong and K.P. Shum, Semilattice structure of rgular cyber groups, Pragmetic Algebra I, India, (2006), 1-12.
• M. Petrich and N. R. Reilly,Completely regular semigroups, John Wiley & Sons, New York, 1999.
• M. Petrich, A structure theorem for completely regular semigroups, Proc. Amer. Math. Soc., 99 (4) (1987), 617-622.
• X. M. Ren and K. P. Shum, The structure of Q-inverse semigroups, J. of Algebra, 325 (2011), 1–17.
• X. M. Ren and K. P. Shum, The structure of superabundant semigroups, Science in China Series A: Mathematics 47(5) (2004), 756–771.
• X. M. Ren and K. P. Shum, On superabundant semigroups whose set of idempotents forms a subsemigroup, Algebra Colloquium 14:2 (2007), 215–228.
• X. M. Ren and K. P. Shum, The structure of L-inverse semigroups, Science in China Series A: Mathematics 49(8) (2006), 1065–1081.
• K. P. Shum, X. M. Ren and Y. Q. Guo, On C-quasiregular semigroups, Communications in Algebra, 27 (19) (1999), 4251-4274.
• Lili Wang and Aifa Wang, Some properties of regular crypto H-abundant groups, Proceedings of The 3rd International conference in Electric and Electronic, (EEJC-13), Atlantis Press, doi:10.2991/eeic-13-2013-97.
• P. S. Venkatsen, Right (left) inverse semigroups, J. Algebra 31 (1974), 209–217.
• M. Yamada, Orthodox semigroups whose idempotents satisfy a certain identity, Semigroup Forum 6 (1973), 113–128.