A Remark about Noncommutative Integral Extensions

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Abstract
Let B be a ring with unity, A a imitai subring of the centre Cof B. Suppose further that B is A-integral. (That is, every element of B satisfies a monic polynomial with coefficients in A.) Under these assumptions, Hoechsmann [2] showed that "contraction to A" is a mapping from: (1)The prime ideals of B onto the prime ideals of A, (2)The maximal ideals of B onto the maximal ideals of A. In this note we show that, under additional assumptions, a noncommutative version of the rest of the Cohen-Seidenberg "going up theorem" can be established.

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