Another Structure of Weakly Left C-wrpp Semigroups

It is known that a left C-wrpp semigroup can
be described as curler structure of a left band and a C-wrpp
semigroup. In this paper, we introduce the class of weakly left
C-wrpp semigroups which includes the class of weakly left C-rpp
semigroups as a subclass. We shall particularly show that the spined
product of a left C-wrpp semigroup and a right normal band is a
weakly left C-wrpp semifroup. Some equivalent characterizations of
weakly left C-wrpp semigroups are obtained. Our results extend that
of left C-wrpp semigroups.

• Enxiao Yuan
• Xiaomin Zhang

• Left C-wrpp semigroup
• left quasi normal regular band
• weakly left C-wrpp semigroup.

[1] J. M. Howie, An introduction to semigroup theory, London: London
Acaemic Press, 1976.
[2] L. Du and K. P. Shum, On left C-wrpp semigroups, Semigroup Forum,
Vol. 67, pp. 373-387,2003.
[3] X. D. Tang, On a theorem of C-wrpp semigroups, Comm. Algebra,
Vol. 25, pp. 1499-1504, 1997.
[4] J. B. Fountain, Right pp monoids with central idempotents, Semigroup
Forum, Vol. 13: 229-237, 1977.
[5] Y. L. Cao, The structure of weakly left C-rpp semigroups, J..Zibo
University, Vol. 2, pp. 3-8, 2000.
[6] P. Y. Zhu, Y. Q. Guo and K. P. Shum, Structure and characterization of
left Clfford semigroups, Sci.China, Ser., Vol..(A)35, pp. 791-805, 1991.
[7] Y. Q. Guo, Structure of weakly left C-semigroups, Chinese Sci.Bull.,
Vol. 41, pp. 462-467, 1996.
[8] Y. Q. Guo, K. P. Shum and P. Y. Zhu, The structure of left C-rpp
semigroups, Semigroup Forum, Vol.50, pp. 9-23, 1995.
[9] X. M. Ren and K. P. Shum, Structure theorem for right pp semigroups
with left central idempotents, Disscuss.Math.Gen.Algebra Appl.,Vol.,
20, pp. 63-75, 2000.
[10] X. M. Zhang, The Structure of Weakly Left C-wrpp semigroups,
International Journal of Computational and Mathematical Sciences, Vol.
2, pp. 170-172, 2008.