# How is called a semigroup…

Does anyone know, how is called a semigroup in which every equation $ax=b$ has only a finite set (maybe empty) of solutions?

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Please give more motiviation and background for the question. – Martin Brandenburg Nov 17 '11 at 16:12
@Martin: I now return to my old article in 1996 with K.Iordjev (you can see it in my homepage). I used such semigroups in it and now would know whether they are some own name. – Boris Novikov Nov 17 '11 at 18:31

Update. It is proved by Ellis in http://www.ams.org/journals/tran/2001-353-04/S0002-9947-00-02704-5/S0002-9947-00-02704-5.pdf that an infinite semigroup T has finite geometric type if and ony if $\beta T\setminus T$ is a right ideal where $\beta T$ is the Stone-Czech compactification of T.