Modules and Comodules pp 169-172
A Note on Polynomial Rings over Nil Rings
Let R be a nil ring with pR = 0 for some prime number p. We show that the polynomial ring R[x,y] in two commuting indeterminates x, y over R cannot be homomorphically mapped onto a ring with identity. This extends, in finite characteristic case, a result obtained by Smoktunowicz  and gives a new approximation, in that case, of a positive solution of Köthe’s problem.
KeywordsNil ring polynomial ring Brown-McCoy radical Köthe’s problem
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