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Answer to Question #17366 in Algebra for Melvin Henriksen

Question #17366
Show that any unit-regular ring R is Dedekind-finite.
Expert's answer
Suppose ab = 1 ∈ R, where R is unit-regular. Write a =aua, where u ∈ U(R). Then 1 = ab = auab= au, so a = u−1 ∈ U(R).

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