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nil and nilpotent ideals
A ring is nil if every element in is nilpotent. Similarly, a one- or two-sided ideal is called nil if each of its elements is nilpotent.
A ring [resp. a one- or two sided ideal ] is nilpotent if [resp. ] for some positive integer .
A ring or an ideal is locally nilpotent if every finitely generated subring is nilpotent.
The following implications hold for rings (or ideals):
Defines:
nil, nil ring, nil ideal, nil right ideal, nil left ideal, nil subring, nilpotent, nilpotent element, nilpotent ring, nilpotent ideal, nilpotent right ideal, nilpotent left ideal, nilpotent subring, locally nilpotent, locally nilpotent ring, locally nilpo
Related:
KoetheConjecture
Type of Math Object:
Definition
Major Section:
Reference
Mathematics Subject Classification
16N40 Nil and nilpotent radicals, sets, ideals, rings- Forums
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