nilpotent subring
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1967 ◽  
Vol 8 (2) ◽  
pp. 89-101 ◽  
Author(s):  
Gerhard Michler

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.


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