Abstract:
Flat modules over rings, acts over semigroups are modules or acts such that functor $A \otimes-$ preserves monomorphisms. A unar, i.e. a set with only an unary operation can be considered as an act over a free cycle semigroup. It is shown that a unar is flat if and only if it is a coproduct of unars, each of which is a line, ray or cycle.
Keywords:act over semigroup, unar, flat unar, tensor poduct of acts.
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