A structure theorem for right pp-semigroups with left central idempotents
Discussiones Mathematicae. General Algebra and Applications, Tome 20 (2000) no. 1, pp. 63-75.

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The concept of strong spined product of semigroups is introduced. We first show that a semigroup S is a rpp-semigroup with left central idempotents if and only if S is a strong semilattice of left cancellative right stripes. Then, we show that such kind of semigroups can be described by the strong spined product of a C-rpp-semigroup and a right normal band. In particular, we show that a semigroup is a rpp-semigroup with left central idempotents if and only if it is a right bin.
Keywords: right pp-semigroups, right zero bands, strong spined products
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Ren, Xue; Shum, Kar-Ping. A structure theorem for right pp-semigroups with left central idempotents. Discussiones Mathematicae. General Algebra and Applications, Tome 20 (2000) no. 1, pp. 63-75. http://geodesic.mathdoc.fr/item/DMGAA_2000_20_1_a5/

[1] J.B. Fountain, Right pp monoids with central idempotents, Semigroup Forum 13 (1977), 229-237.

[2] J.B. Fountain, Adequate semigroups, Proc. Edinburgh Math. Soc., 22 (1979), 113-125.

[3] J.B. Fountain, Abundant semigroups, Proc. London Math. Soc., (3) 44 (1982), 103-129.

[4] Y.Q. Guo, K.-P. Shum and P.Y. Zhu, The structure of left C-rpp-semigroups, Semigroup Forum 50 (1995), 9-23.

[5] Y.Q. Guo, Weakly left C-semigroups, Science Bull. (China), 41, (1996), 462-467.

[6] X.J. Guo, Y.Q. Guo and K.-P. Shum, Semi-spined structure of left C-a-semigroups, 'Semigroups', Springer-Verlag, Singapore 1998, 157-166.

[7] X.J. Guo, K.-P. Shum and Y.Q. Guo, On perfect C-rpp-semigroups, to appear.

[8] J.M. Howie, An introduction to semigroups theory, Academic Press, New York 1976.

[9] N. Kimura, Note on idempotent semigroups, I, Proc. Japan Acad. 34 (1958), 113-114.

[10] G.B. Preston, Semi-direct products of semigroups, 'Procedings of the International Conference, Words, Languages and Combinatorics (II)', World Scientific Japan, Kyoto, Singapore 1992, 320-327.

[11] X.M. Ren, K.-P. Shum and Y.Q. Guo, On spined product of quasi-rectangular groups, Algebra Colloquim 4 (1997), 187-194.

[12] K.-P. Shum and Y.Q. Guo, Regular semigroups and their generlizations, 'Rings, Groups and Algebras', Marcel Dekker, Inc., New York 1996, 181-226.

[13] K.-P. Shum and X.M. Ren, Abundant semigroups with left central idempotents, Pure Math. Appl., 10 (1999), 109-113.