About: Dedekind-finite ring

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A ring is said to be a Dedekind-finite ring if ab = 1 implies ba = 1 for any two ring elements a and b. In other words, all one-sided inverses in the ring are two-sided. These rings have also been called directly finite rings and von Neumann finite rings.

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  • A ring is said to be a Dedekind-finite ring if ab = 1 implies ba = 1 for any two ring elements a and b. In other words, all one-sided inverses in the ring are two-sided. These rings have also been called directly finite rings and von Neumann finite rings. (en)
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  • A ring is said to be a Dedekind-finite ring if ab = 1 implies ba = 1 for any two ring elements a and b. In other words, all one-sided inverses in the ring are two-sided. These rings have also been called directly finite rings and von Neumann finite rings. (en)
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  • Dedekind-finite ring (en)
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