Modules in which every surjective endomorphism has a μ-small kernel

In this paper we introduce the notion of μ -Hopfian modules which is a proper generalization of that of Hopfian modules. We give some characterizations and properties of these modules. We prove that a ring R is semisimple if and only if every R -module is μ -Hopfian. Moreover, we prove that the μ -H...

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Published in:Annali dell'Università di Ferrara. Sezione 7. Scienze matematiche 2020-11, Vol.66 (2), p.325-337
Main Authors: El Moussaouy, Abderrahim, Ziane, M’Hammed
Format: Article
Language:English
Subjects:
Algebraic Geometry
Analysis
Geometry
History of Mathematical Sciences
Mathematics
Mathematics and Statistics
Modules
Numerical Analysis
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description In this paper we introduce the notion of μ -Hopfian modules which is a proper generalization of that of Hopfian modules. We give some characterizations and properties of these modules. We prove that a ring R is semisimple if and only if every R -module is μ -Hopfian. Moreover, we prove that the μ -Hopfian property is Morita invariant. Further, we prove an analogue to Hilbert’s basis Theorem for μ -Hopfian modules.
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subjects Algebraic Geometry
Analysis
Geometry
History of Mathematical Sciences
Mathematics
Mathematics and Statistics
Modules
Numerical Analysis
title Modules in which every surjective endomorphism has a μ-small kernel
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