A note on the stability of pure-injective modules

Autor: Chunhua Yang, Zhaoyong Huang
Rok vydání: 2017
Předmět:
Zdroj: Communications in Algebra. 45:5068-5072
ISSN: 1532-4125
0092-7872
Popis: 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 ExtRn(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⊗RM is pure-injective; and if R is left coherent, then the left S-module TornR(N,M) is pure-injective for any n≥1.
Databáze: OpenAIRE