科研之友
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摘要
Let R be a ring. Then a left R-module N is pure-injective if and only if HomR(M,N) is a pure-injective left S-module for any ring S and any (R,S)-bimodule RMS. If R is a commutative ring and M,N are R-modules with N pure-injective, then ExtnR(M,N) is a pure-injective R-module for any n >= 0. Let R and S be rings and let SNR be an (S,R)-bimodule and M a finitely presented left R-module. If N is pure-injective as a left S-module, then the left S-module N (circle times R) M is pure-injective; and if R is left coherent, then the left S-module Tor(n)(R)(N,M) is pure-injective for any n >= 1.
