Example of an Injective Module which is Not Nice
Canadian mathematical bulletin, Tome 17 (1974) no. 1, pp. 133-134
Voir la notice de l'article provenant de la source Cambridge University Press
In [1] Lambek calls the injective R-module I nice if every torsionfree factor module of the ring of quotients Q of R with respect to lis divisible. If lis nice then g is a dense subring of the bicommutator BicRI of I with respect to the finite topology (see [1, Proposition 2]). We now give an example of an injective R-module over an Artinian ring R which is not nice. Since R is Artinian, Q=BicR I, by Proposition B of [1].Before we give the example, we state the following, which depends on [2] for terminology.
Michler, Gerhard O. Example of an Injective Module which is Not Nice. Canadian mathematical bulletin, Tome 17 (1974) no. 1, pp. 133-134. doi: 10.4153/CMB-1974-028-4
@article{10_4153_CMB_1974_028_4,
author = {Michler, Gerhard O.},
title = {Example of an {Injective} {Module} which is {Not} {Nice}},
journal = {Canadian mathematical bulletin},
pages = {133--134},
year = {1974},
volume = {17},
number = {1},
doi = {10.4153/CMB-1974-028-4},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1974-028-4/}
}
[1] 1. Lambek, J., Bicommutators of nice infectives, J. Algebra (to appear). Google Scholar
[2] 2. Lambek, J. and Michler, G., The torsion theory at a prime ideal of a right Noetherian ring, (submitted for publication). Google Scholar
[3] 3. Lambek, J., Torsion theories, additive semantics and rings of quotients, Springer Lecture Note in Math. 177, 1971. Google Scholar
Cité par Sources :