Epis and monos which must be isos

David J. Fieldhouse

International Journal of Mathematics and Mathematical Sciences, 1984, vol. 7, 1-6

Abstract:

Orzech [1] has shown that every surjective endomorphism of a noetherian module is an isomorphism. Here we prove analogous results for injective endomorphisms of noetherian injective modules, and the duals of these results. We prove that every injective endomorphism, with large image, of a module with the descending chain condition on large submodules is an isomorphism, which dualizes a result of Varadarajan [2]. Finally we prove the following result and its dual: if p is any radical then every surjective endomorphism of a module M , with kernel contained in p M , is an isomorphism, provided that every surjective endomorphism of p M is an isomorphism.

Date: 1984
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/7/289592.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/7/289592.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:289592

DOI: 10.1155/S0161171284000557

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().