Rings whose modules form few torsion classes
BJ Gardner - Bulletin of the Australian Mathematical Society, 1971 - cambridge.org
Bulletin of the Australian Mathematical Society, 1971•cambridge.org
… Throughout this note all rings are associative, with identity, and except where otherwise
specified, all modules are left, unital modules. A torsion class of modules is a non-void class
closed under homomorphic images, extensions and direct sums. A torsion class which is
also closed under submodules is called hereditary. …
specified, all modules are left, unital modules. A torsion class of modules is a non-void class
closed under homomorphic images, extensions and direct sums. A torsion class which is
also closed under submodules is called hereditary. …
Characterizations are obtained of rings R such that the only torsion classes (respectively, hereditary torsion classes) of left unital R-modules are {0} and the class of all modules.
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