# Answer to Question #16660 in Abstract Algebra for Melvin Henriksen

Question #16660

Show that any left noetherian ring R is Dedekind-finite.

Expert's answer

Since

*R*is a noetherian module, it is hopfian, and left regular module*R*is hopfian iff*R*is Dedekind – finite, so*R*is Dedekind – finite.
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