If R is a ring with identity and M is a left R-module then it is well known that the following statements are equivalent:
(1) M is flat.
(2) The functor—⊗ M preserves embeddings of right ideals into R.
This paper investigates situations in which the analogous statements are equivalent in the context of S-sets over a monoid S.
Bulman-Fleming, Sydney and McDowell, Kenneth, "Monoids over which all weakly flat acts are flat" (1990). Mathematics Faculty Publications. 4.