On left absolutely flat monoids (Q910501)

A monoid is called left absolutely flat if all left S-systems B are flat, i.e. the functor -\(\otimes B\) takes monomorphisms into injective mappings. The authors show the equivalence of the following: i) S is left absolutely flat, ii) all finitely generated left S-systems are flat, iii) all finitely presented left S-systems are flat. Moreover the authors specify a subclass of finitely presented S-systems and prove that S is left absolutely flat if each object in the subclass preserves specific monomorphisms. One can use this result to describe left absolutely flat monoids in terms of rather complicated zigzags (S-tossings) of elements.