If S is a partially ordered monoid then a right S-poset is a poset A on which S acts from the right in such a way that the action is compatible both with the order of S and A. By regular weak injectivity properties we mean injectivity properties with respect to all regular monomorphisms (not all monomorphisms) from different types of right ideals of S to S. We give an alternative description of such properties which uses systems of equations. Using these properties we prove several so-called homological classification results which generalize the corresponding results for (unordered) acts over (unordered) monoids proved by Victoria Gould in the 1980’s.
 S. Bulman-Fleming and V. Laan: “Lazard’s theorem for S-posets”, Math. Nachr., Vol. 278(15), (2005), pp. 1743–1755. http://dx.doi.org/10.1002/mana.20031033810.1002/mana.200310338Search in Google Scholar
 S. Bulman-Fleming and M. Mahmoudi: “The category of S-posets”, Semigroup Forum, Vol. 71, (2005), pp. 443–461. http://dx.doi.org/10.1007/s00233-005-0540-y10.1007/s00233-005-0540-ySearch in Google Scholar
 G. Czédli and A. Lenkehegyi: “On classes of ordered algebras and quasiorder distributivity”, Acta Sci. Math. (Szeged), Vol. 46, (1983), pp. 41–54. Search in Google Scholar
 V.A.R. Gould: “The characterization of monoids by properties of their S-systems”, Semigroup Forum, Vol. 32, (1985), pp. 251–265. Search in Google Scholar
 V.A.R. Gould: “Divisible S-systems and R-modules”, Proc. Edinburgh Math. Soc. II, Vol. 30, (1987), pp. 187–200. http://dx.doi.org/10.1017/S001309150002826110.1017/S0013091500028261Search in Google Scholar
 X. Shi, Z. Liu, F. Wang and S. Bulman-Fleming: “Indecomposable, projective and flat S-posets”, Comm. Algebra, Vol. 33(1), (2005), pp. 235–251. Search in Google Scholar
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