Vol. 35, No. 1, 1970

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On partial homomorphisms of semigroups

B. D. Arendt and C. J. Stuth

Vol. 35 (1970), No. 1, 7–9

Let S be a semigroup and T be a semigroup with zero (T = T0). An ideal extension of S by T is a semigroup V containing S as an ideal and such that the Rees quotient V∕S is isomorphic to T. A mapping α from T = T −{0} into S is said to be a partial homomorphism, if t1,t2 T,t1t20 implies (f1,t2)α = (t1α)(t2α). Every partial homomorphism from τinto S gives rise to an ideal extension of )S by T. Further, in certain cases every ideal extension of S by T is obtained in this way. In this paper a characterization is given for all partial homomorphisms from τinto S.

Mathematical Subject Classification
Primary: 20.93
Received: 7 October 1969
Published: 1 October 1970
B. D. Arendt
C. J. Stuth