Levitzky's theorem

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. Levitzky's theorem is one of the many results suggesting the veracity of the Köthe conjecture.

See also

• Nilpotent ideal
• Köthe conjecture
• Jacobson radical

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. MR 0033799.
• Levitzki, Jakob (1945), "Solution of a problem of G. Koethe", American Journal of Mathematics, 67: 437–442, doi:10.2307/2371958, ISSN 0002-9327, MR 0012269
• Utumi, Yuzo (1963), "Mathematical Notes: A Theorem of Levitzki", The American Mathematical Monthly, 70 (3): 286, doi:10.2307/2313127, ISSN 0002-9890, MR 1532056