满子范畴的反变有限性与同调满同态

The contravariant finiteness of the full subcategories and the homological epimorphisms

讨论域k上的代数A,B的满子范畴p<∞(A)和p<∞(B)的关系,研究它们的反变有限性之间的关系,得到结论:如果域k上的代数A,B之间存在同调满同态φ:A→B,若B作为A-模是投射维数有限的,则p<∞(A)反变有限可以推出p<∞(B)也反变有限.

This paper studied the relation of the full subcategories p^<∞(A)and p^<∞(B)of A-mod and B-mod,and the relation of the contravariant finiteness of p^<∞(A)and p^<∞(B).The following result was proved.Let A,B be two algebras over the field k,if the projective dimension of B was finite as an A-module and p^<∞(A)was contravariantly finite in A-mod,then p^<∞(B)was contravariantly finite in B-mod.