Vol. 67, No. 2, 1976

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The generalized translational hull of a semigroup

John Keith Luedeman

Vol. 67 (1976), No. 2, 489–507
Abstract

For a pair (,) consisting of a right quotient filter and left quotient filter on the semigroup S, a translational hull Ω(S : ,) is constructed. The results of Grillet and Petrich hold for Ω(S : ,).

Specializing and one obtains the usual translational hull Ω(S) of S and the semigroup of quotients Q(S) of S due to Hinkle and McMorris. These results are applied to a weakly reductive semigroup S to show that Ω(S) = Ω(Sn) for any positive integer n.

Mathematical Subject Classification 2000
Primary: 20M10
Milestones
Received: 11 June 1975
Revised: 15 April 1976
Published: 1 December 1976
Authors
John Keith Luedeman