When is the radical associated with a module a torsion?
Matematičeskie zametki, Tome 16 (1974) no. 1, pp. 41-48
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For an arbitrary $R$-module $M$ we consider the radical (in the sense of Maranda)$\mathfrak G_M, namely, the largest radical among all radicals $\mathfrak G$, such that$\mathfrak G(M)=0$. We determine necessary and sufficient on $M$ in order for the radical $\mathfrak G_M$ to be a~torsion. In particular,$\mathfrak G_M$ is a~torsion if and only if $M$ is a pseudo-injective module.
@article{MZM_1974_16_1_a4,
author = {A. I. Kashu},
title = {When is the radical associated with a~module a~torsion?},
journal = {Matemati\v{c}eskie zametki},
pages = {41--48},
year = {1974},
volume = {16},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1974_16_1_a4/}
}
A. I. Kashu. When is the radical associated with a module a torsion?. Matematičeskie zametki, Tome 16 (1974) no. 1, pp. 41-48. http://geodesic.mathdoc.fr/item/MZM_1974_16_1_a4/