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On maximal nilpotent subrings of right Noetherian rings

Published online by Cambridge University Press:  18 May 2009

Gerhard Michler
Gerhard Michler
Affiliation:
Johann Wolfgang Goethe UniversitätFrankfurt
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Applying Hopkins's Theorem asserting that each unitary right Artinian ring is right Noetherian, G. Köthe and K. Shoda proved the following theorem (cf. Köthe [7], p. 360, Theorem 1 and p. 363, Theorem 5): If R is a unitary right Artinian ring, then the following statements hold:

(i) Each nilpotent subring of R is contained in a maximal nilpotent subring of R.

(ii) The intersection of all maximal nilpotent subrings of R is the maximal nilpotent twosided ideal of R.

(iii) All maximal nilpotent subrings of R are conjugate.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 8 , Issue 2 , July 1967 , pp. 89 - 101
Copyright
Copyright © Glasgow Mathematical Journal Trust 1967

References

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