Mathematicae General Algebra and Applications 20(1) (2000) 63-75
STRUCTURE THEOREMS FOR RIGHT pp-SEMI-GROUPS WITH LEFT CENTRAL IDEMPOTENTS
Xue Ming Ren and Kar-Ping Shum
Department of Mathematics, The Chinese University of
Shatin, N.T., Hong Kong
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.
1991 Mathematics Subject Classification: 20M10.
|||J.B. Fountain, Right pp monoids with central idempotents, Semigroup Forum 13 (1977), 229-237.|
|||J.B. Fountain, Adequate semigroups, Proc. Edinburgh Math. Soc., 22 (1979), 113-125.|
|||J.B. Fountain, Abundant semigroups, Proc. London Math. Soc., (3) 44 (1982), 103-129.|
|||Y.Q. Guo, K.-P. Shum and P.Y. Zhu, The structure of left C-rpp-semigroups, Semigroup Forum 50 (1995), 9-23.|
|||Y.Q. Guo, Weakly left C-semigroups, Science Bull. (China), 41, (1996), 462-467.|
|||X.J. Guo, Y.Q. Guo and K.-P. Shum, Semi-spined structure of left C-a -semigroups, p. 157-166 in: '134 Semigroups", Springer-Verlag, Singapore 1998.|
|||X.J. Guo, K.-P. Shum and Y.Q. Guo, On perfect C-rpp-semigroups, to appear.|
|||J.M. Howie, An introduction to semigroups theory, Academic Press, New York 1976.|
|||N. Kimura, Note on idempotent semigroups, I, Proc. Japan Acad. 34 (1958), 113-114.|
|||G.B. Preston, Semi-direct products of semigroups, p. 320-327 in: '134Procedings of the International Conference, Words, Languages and Combinatorics (II)", World Scientific Japan, Kyoto, Singapore 1992.|
|||X.M. Ren, K.-P. Shum and Y.Q. Guo, On spined product of quasi-rectangular groups, Algebra Colloquim 4 (1997), 187-194.|
|||K.-P. Shum and Y.Q. Guo, Regular semigroups and their generlizations, p. 181-226 in: '134Rings, Groups and Algebras", Marcel Dekker, Inc., New York 1996.|
|||K.-P. Shum and X.M. Ren, Abundant semigroups with left central idempotents, Pure Math. Appl., 10 (1999), 109-113.|
Received 29 August 1998
Revised 15 June 1999
Revised 25 February 2000