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Levitzky's theorem

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In mathematics, more specifically ring theory and the theory of nil ideals, Levitzky's theorem, named after Jacob Levitzki, states that in a right Noetherian ring, every nil one-sided ideal is necessarily nilpotent.[1][2] Levitzky's theorem is one of the many results suggesting the veracity of the Köthe conjecture. The first proof of this theorem was due to Utumi.[3]

Proof

See also

Notes

  1. ^ Herstein, Theorem 1.4.5, p. 37
  2. ^ Isaacs, Theorem 14.38, p. 210
  3. ^ Herstein, p. 38

References

  • I. Martin Isaacs (1993). Algebra, a graduate course (1st edition ed.). Brooks/Cole Publishing Company. ISBN 0-534-19002-2. {{cite book}}: |edition= has extra text (help)
  • I.N. Herstein (1968). Noncommutative rings (1st edition ed.). The Mathematical Association of America. ISBN 0-88385-015-X. {{cite book}}: |edition= has extra text (help)
  • J. Levitzki (1950). "On multiplicative systems". Compositio Math. 8: 76--80.
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