On partial homomorphisms of semigroups
B. D. Arendt, Charles J. Stuth · Pacific Journal of Mathematics · 1970
Let S be a semigroup and T be a semigroup with zero (Γ=Γ°). 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 a from T*=T-{0} into S is said to be a partial homomorphism, if t u t 2 e T*, tit 2 Φ 0 implies (tit 2 )a=(tia)(t 2 a).Every partial homomorphism from T* into 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 T* into S.