Abstract
In this paper we continue the study of Tbk-semigroups [1]. We define a weak Tbk-semigroup as an algebra (s,·,∩) which satisfies (A1) a(bc) = (ab)c, (A2) (S, ∩) is a semilattice, (A3) × (a ∩ b) y = xay ∩ xby, (A4) a ∈ (a ∩ b) S ∩ S (a ∩ b) . We shall prove that every weak Tbk-semigroup can be embedded into a Tbk-semigroup with 1, and we shall show that the theory of [1] can be developed already in weak Tbk-semigroups.
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Bosbach, B.:Zur Theorie der Teilbarkeitshalbgruppen. Semigroup Forum 3 (1971),1–30
Clifford,A.H. G.B. Preston:The algebraic theory of semigroups, Math. Surveys No 7, Amer.Math.Soc.,Providence; Vol.I,1961, Vol.II,1967
Fuchs, L.:Teilweise geordnete algebraische Strukturen, Studia Math.,Vandenhoek und Rupprecht, Oldenburg; 1966
Merlier,Th.:Sur les demi-groupes reticules et les o-demi-groupes. Semigroup Forum 2 (1971), no.1, 64–70
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Klaus Wagner zum 65.Geburtstag
Über den Inhalt dieser Note berichtete der Autor verschiedene Male , zuletzt im Juni 1974 an der T.U. München.
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Bosbach, B. Schwache Teilbarkeitshalbgruppen. Semigroup Forum 12, 119–135 (1976). https://doi.org/10.1007/BF02195916
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DOI: https://doi.org/10.1007/BF02195916