On generalized q.f.d. modules
Saleh, Mohammad ; Jain, S. K. ; López-Permouth, Sergio R.
Archivum Mathematicum, Tome 041 (2005), p. 243-251 / Harvested from Czech Digital Mathematics Library
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A right $R$-module $M$ is called a generalized q.f.d. module if every M-singular quotient has finitely generated socle. In this note we give several characterizations to this class of modules by means of weak injectivity, tightness, and weak tightness that generalizes the results in [sanh1], Theorem 3. In particular, it is shown that a module $M$ is g.q.f.d. iff every direct sum of $M$-singular $M$-injective modules in ${\sigma [M]}$ is weakly injective iff every direct sum of $M$-singular weakly tight is weakly tight iff every direct sum of the injective hulls of $M$-singular simples is weakly $R$-tight.

Publié le : 2005-01-01
Classification:  16D10,  16D50,  16D60,  16D70,  16D90 
@article{107955,
     author = {Mohammad Saleh and S. K. Jain and Sergio R. L\'opez-Permouth},
     title = {On generalized q.f.d. modules},
     journal = {Archivum Mathematicum},
     volume = {041},
     year = {2005},
     pages = {243-251},
     zbl = {1114.16004},
     mrnumber = {2188380},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107955}
}

Saleh, Mohammad; Jain, S. K.; López-Permouth, Sergio R. On generalized q.f.d. modules. Archivum Mathematicum, Tome 041 (2005) pp. 243-251. http://gdmltest.u-ga.fr/item/107955/

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