On Functional Representations of a Ring without Nilpotent Elements

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Abstract
In [3, p. 149], J. Lambek gives a proof of a theorem, essentially due to Grothendieck and Dieudonne, that if R is a commutative ring with 1 then R is isomorphic to the ring of global sections of a sheaf over the prime ideal space of R where a stalk of the sheaf is of the form R/0P, for each prime ideal P, and . In this note we will show, this type of representation of a noncommutative ring is possible if the ring contains no nonzero nilpotent elements.

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