Hopficity and duo rings

Ulrich Albrecht () and Francisco Javier Santillán-Covarrubias ()
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Ulrich Albrecht: Auburn University
Francisco Javier Santillán-Covarrubias: Kennesaw State University

Indian Journal of Pure and Applied Mathematics, 2021, vol. 52, issue 2, 369-374

Abstract: 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.

Keywords: Non-commutative Ring Theory; Chain and Duo Rings; Hopfian Modules; 16L30; 16P70; 16U80 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13226-021-00144-2

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