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Epis and monos which must be isos. (English) Zbl 0576.16035

A surjective (or injective) linear transformation of a finite dimensional vector space to itself is an isomorphism. This result has been generalized in various ways to certain modules over rings by W. V. Vasconcelos, M. Orzech and K. Varadarajan. There are some further observations and generalizations collected in this note. For example: An injective endomorphism, with large image, of a module with d.c.c. on large submodules is an isomorphism. The author also points out that these results come in pairs, one being the dual of the other.
Reviewer: H.-H.Brungs

MSC:

16W20 Automorphisms and endomorphisms
16D80 Other classes of modules and ideals in associative algebras
16Nxx Radicals and radical properties of associative rings
16P40 Noetherian rings and modules (associative rings and algebras)
16P20 Artinian rings and modules (associative rings and algebras)
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