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Practice problem

Commutative Algebra

By Victor Wang

Let RR be a ring with non-invertible elements xx and yy such that x+y=1x+y=1 and (xy)n=0(xy)^n = 0 for some positive integer nn.

Must RR have a nontrivial idempotent ee, i.e. a solution to e2=ee^2=e with e≠0,1e\neq0,1?

Choose one answer

Type a concept, like “slope” or “photosynthesis”.

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