A structure theorem for right pp-semigroups with left central idempotents

Xue Ming Ren; Kar-Ping Shum

Discussiones Mathematicae - General Algebra and Applications (2000)

  • Volume: 20, Issue: 1, page 63-75
  • ISSN: 1509-9415

Abstract

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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.

How to cite

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Xue Ming Ren, and Kar-Ping Shum. "A structure theorem for right pp-semigroups with left central idempotents." Discussiones Mathematicae - General Algebra and Applications 20.1 (2000): 63-75. <http://eudml.org/doc/287682>.

@article{XueMingRen2000,
abstract = {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.},
author = {Xue Ming Ren, Kar-Ping Shum},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {right pp-semigroups; right zero bands; strong spined products; right -semigroups; principal right ideals; left central idempotents; strong semilattices; direct products; left cancellative monoids},
language = {eng},
number = {1},
pages = {63-75},
title = {A structure theorem for right pp-semigroups with left central idempotents},
url = {http://eudml.org/doc/287682},
volume = {20},
year = {2000},
}

TY - JOUR
AU - Xue Ming Ren
AU - Kar-Ping Shum
TI - A structure theorem for right pp-semigroups with left central idempotents
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2000
VL - 20
IS - 1
SP - 63
EP - 75
AB - 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.
LA - eng
KW - right pp-semigroups; right zero bands; strong spined products; right -semigroups; principal right ideals; left central idempotents; strong semilattices; direct products; left cancellative monoids
UR - http://eudml.org/doc/287682
ER -

References

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  1. [1] J.B. Fountain, Right pp monoids with central idempotents, Semigroup Forum 13 (1977), 229-237. Zbl0353.20051
  2. [2] J.B. Fountain, Adequate semigroups, Proc. Edinburgh Math. Soc., 22 (1979), 113-125. Zbl0414.20048
  3. [3] J.B. Fountain, Abundant semigroups, Proc. London Math. Soc., (3) 44 (1982), 103-129. Zbl0481.20036
  4. [4] Y.Q. Guo, K.-P. Shum and P.Y. Zhu, The structure of left C-rpp-semigroups, Semigroup Forum 50 (1995), 9-23. Zbl0821.20046
  5. [5] Y.Q. Guo, Weakly left C-semigroups, Science Bull. (China), 41, (1996), 462-467. 
  6. [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. Zbl0986.20058
  7. [7] X.J. Guo, K.-P. Shum and Y.Q. Guo, On perfect C-rpp-semigroups, to appear. Zbl0989.20048
  8. [8] J.M. Howie, An introduction to semigroups theory, Academic Press, New York 1976. 
  9. [9] N. Kimura, Note on idempotent semigroups, I, Proc. Japan Acad. 34 (1958), 113-114. Zbl0081.25502
  10. [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. Zbl0900.20124
  11. [11] X.M. Ren, K.-P. Shum and Y.Q. Guo, On spined product of quasi-rectangular groups, Algebra Colloquim 4 (1997), 187-194. Zbl0887.20027
  12. [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. [13] K.-P. Shum and X.M. Ren, Abundant semigroups with left central idempotents, Pure Math. Appl., 10 (1999), 109-113. Zbl0938.20047

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