Bicommutators of Cofaithful, Fully Divisible Modules
Canadian journal of mathematics, Tome 23 (1971) no. 2, pp. 202-213
Voir la notice de l'article provenant de la source Cambridge University Press
We define below a notion for modules which is dual to that of faithful, and a notion of “fully divisible” which generalizes that of injectivity. We show that the bicommutator of a cofaithful, fully divisible left R-module is isomorphic to a subring of Qmax(R), the complete ring of left quotients of R.In recent papers, Goldman [2] and Lambek [3] investigated rings of left quotients of a ring R constructed with respect to torsion radicals. It is known that every ring of left quotients of R is isomorphic to the bicommutator of an appropriate injective left R-module. We investigate below subrings of rings of quotients which are determined by radicals rather than torsion radicals, and show that any such ring can be constructed as the bicommutator of a fully divisible left R-module.
Beachy, John A. Bicommutators of Cofaithful, Fully Divisible Modules. Canadian journal of mathematics, Tome 23 (1971) no. 2, pp. 202-213. doi: 10.4153/CJM-1971-020-8
@article{10_4153_CJM_1971_020_8,
author = {Beachy, John A.},
title = {Bicommutators of {Cofaithful,} {Fully} {Divisible} {Modules}},
journal = {Canadian journal of mathematics},
pages = {202--213},
year = {1971},
volume = {23},
number = {2},
doi = {10.4153/CJM-1971-020-8},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1971-020-8/}
}
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