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Semigroup Forum

, Volume 12, Issue 1, pp 137–143 | Cite as

Zur Struktur Der Inversen Teilbarkeits-Halbgruppen

  • Bruno Bosbach
Research Article

Abstract

In this paper we study inverse Tbk-semigroups [cf.1,2.]. We shall show that every inverse Tbk-semigroup is a subdirect product of 1-groups with or without 0, and we shall give necessary and sufficient conditions for (S,·,∩) to be a direct product of an 1-group and a distributive lattice. The second main result is that a Tbk-semigroup can be embedded into an inverse Tbk-semigroup iff as = ab = bb ⇒ a = b and acx = acy ⇔ axc = ayc.

Originally this paper was part of [2]. It was separated from [2] at the suggestion of the referee.

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Literaturverzeichnis

  1. [1]
    Bosbach,B.:Zur Theorie der Teilbarkeitshalbgruppen. Semigroup Forum 3 (1971), 1–30Google Scholar
  2. [2]
    Bosbach,B.:Schwache Teilbarkeitshalbgruppen. Semigroup Forum, 2 (1976), 119–135.Google Scholar
  3. [3]
    Clifford,A.H. G.B.Preston:The algebraic theory of semigroups, Math. Surveys No 7, Amer.Math.Soc.,Providence; Vol.I, 1961, Vol.II,1 967Google Scholar
  4. [4]
    Fuchs,L.:Teilweise geordnete algebraische Strukturen, Studia Math.,Vandenhoeck & Rupprecht, Oldenburg; 1966Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1976

Authors and Affiliations

  • Bruno Bosbach
    • 1
  1. 1.G.H.KasselB.R.Deutschland

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