Hopficity and duo rings
Department
Mathematics
Document Type
Article
Publication Date
6-1-2021
Abstract
The aim of this paper is to study the Hopfian property in the context of chain and duo rings. For such rings, we characterize Hopfian free modules and show that a direct sum of cyclic R-modules is Hopfian if and only if the sum is finite. This allows us to show that finitely generated modules over a local right duo ring, which has the FGC-property, are Hopfian and cancel in direct sums. Moreover, being finitely, hopficity, and the cancellation property are equivalent for modules over Artinian rings.
Journal Title
Indian Journal of Pure and Applied Mathematics
Journal ISSN
00195588
Volume
52
Issue
2
First Page
369
Last Page
374
Digital Object Identifier (DOI)
10.1007/s13226-021-00144-2
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