F－半完备环与F－半完备模

F-SEMI-PERFECT RINGS AND F-SEMI-PERFECT MODULES

本文给出了Ｆ－半备完环的一个刻划：环Ｒ是Ｆ－半完备的当且仅当对任意有限生成左理想Ｒα＿１＋Ｒα＿２＋…＋Ｒα＿ｎ，，其中α＿ｉ∈Ｒ（ｉ＝１，２，…，ｎ）．Ｒ／（Ｒα＿１＋Ｒα＿２＋…＋Ｒα＿ｎ）均有投射覆盖。并把它推广到模上，此外，还得到了投射模的自同态环是半单环的充要条件。

n this paper, a characterization of F-semi-perfect rings is given, whichstates a ring R is F-semi-perfect iff R/Rα_1 +Rα_2+…+Rα_n has a P.C.for anyα_1,α_3,…,α_n∈R and generalize it to modules. On the other hand, we giveaequivalent condition for the endomorphism ring S of a projective module P tobe semisimple