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2000 | 20 | 1 | 63-75
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Kategorie tematyczne
Rocznik
Tom
20
Numer
1
Strony
63-75
Opis fizyczny
Daty
wydano
2000
poprawiono
1998-02-25
otrzymano
1998-08-29
poprawiono
1999-06-15
Twórcy
autor
  • Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong
  • Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong
Bibliografia
  • [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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1006
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