Dedekind-finite_ring

Dedekind-finite ring

Dedekind-finite ring

Mathematical concept

In mathematics, 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[1] and von Neumann finite rings.[2]

Properties

References

  1. [1]
    Goodearl, Kenneth (1976). Ring Theory: Nonsingular Rings and Modules. CRC Press. pp. 165–166. ISBN 978-0-8247-6354-1.
  2. [2]
    Lam, T. Y. (2012-12-06). A First Course in Noncommutative Rings. Springer Science & Business Media. ISBN 978-1-4684-0406-7.

See also


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