有限置换模自同态环的可分性质

SEPARATIVITY OF ENDOMORPHISM RINGS OF MODULES WITH FINITE EXCHANGE PROPERTY

设Q是有限置换右R模,则End_R(Q)是可分环当且仅当对所有A,B∈FP(Q),A AA B B B A≤ B或 B≤A,作为应用得到了 End_R(P Q)是可分环当且仅当End_R P和End_R Q为可分环,其中P,Q为有限置换右R模。

It is shown that if Q is a right R-module with finite exchange property then EndRQ is a separative ring if and only if A A = A B B B A B or B A for all A, 5 ∈ FP(Q). As an application, the author proves that if P and Q are right R-modules with finite exchange property, then EndR(P Q) is a separative ring if and only if so are EndRP and EndRQ.