PlanetMath: Koethe conjecture

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Koethe conjecture

(Conjecture)

The Koethe Conjecture is the statement that for any pair of nil right ideals and in any ring , the sum is also nil.

In particular, this means that the Koethe conjecture is true for commutative rings.

It has been shown to be true for many classes of rings, but the general statement is still unproven, and no counter example has been found.

"Koethe conjecture" is owned by mclase.

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Cross-references: classes, commutative rings, properties of nil and nilpotent ideals, easy to see, two-sided ideal, nil, sum, ring, nil right ideals
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This is version 2 of Koethe conjecture, born on 2002-12-08, modified 2004-02-28.
Object id is 3691, canonical name is KoetheConjecture.
Accessed 2198 times total.

Classification:

16N40 (Associative rings and algebras :: Radicals and radical properties of rings :: Nil and nilpotent radicals, sets, ideals, rings)

Pending Errata and Addenda

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