摘要
LetS be a semigroup andE the set of all idempotents inS. LetS-Act be the category of allS-acts. LetC be a full subcategory ofS-Act which containss S and is closed under coproducts and summands. It is proved that, inC, anS-actP is projective and unitary if and only ifP? ? j? I Se i ,e i ?E. In particular,P is a projective, indecomposable and unitary object if and only ifP ?Se for somee ∈E. These generalize some results obtained by Knauer and Talwar.
Let S be a semigroup and E the set of all idempotents in S. Let S-Act be the category of all S-acts. Let (?) be a full subcategory of S-Act which contains _sS and is closed under coproducts and summands. It is proved that, in (?), an S-act P is projective and unitary if and only if P (?) Ц_i∈1 Se_i, e_i∈E. In particular, P is a projective, indecomposable and unitary object if and only if P (?) Se for some e∈E. These generalize some results obtained by Knauer and Talwar.
基金
Research partially supported by a UGC (HK) (Grant No. 2160092)
