| In this paper,we first investigate some basic properties of Rees short exact se-quences.Next,on the Rees short exact sequence 0→Xs→YS→Zs→0,we study the characterizations of flat properties(free,weakly projective,R-torsion free,(strong)faithful,Condition(E’),(E’),(P’),(PA),C(P)-act,P-regular,strong P-cycle,strongly flat)and injective properties(injective,co-free,divisible,princi-pally weakly injective,n-principally weakly injective)over a monoid S with zero.At last,we prove that some properties(po-torsion free,po-flat,principally weakly po-flat,Condition(Pw),Condition(PWPw)and so on)of Y can be transferred to X in the Rees short exact sequence 0→Xs→YS→ZS→0 of S-posets if it is left split.Similarly,Y can be transferred to Z when the sequence is right split. |
