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ON $IF$-RINGS
Keywords:
strongly cohopfian module, $IF$-ring, artinian ring with principal ideals, semilocal ring, quasi-Frobenius ring, Köthe ringDOI:
https://doi.org/10.17654/0972555524004Abstract
Let $R$ denote an associative ring with unit Then it is well known that any artinian $R$-module is strongly cohopfian, but the converse is not true, in general. The aim of this work is to study some classes of rings $R$ for which strongly cohopfian modules and artinian modules coincide. These kinds of rings are said to be $IF$-rings. We characterize the $IF$-rings which are artinian principal ideals, the $IF$-rings semilocal, the quasi-Frobenius $IF$-rings and the Köthe $IF$-rings.
Received: September 12, 2023
Accepted: November 8, 2023
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