Geodesic
A Remark about Noncommutative Integral Extensions
Canadian mathematical bulletin, Tome 13 (1970) no. 3, pp. 359-361

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Heinicke, A. G. A Remark about Noncommutative Integral Extensions. Canadian mathematical bulletin, Tome 13 (1970) no. 3, pp. 359-361. doi: 10.4153/CMB-1970-067-0
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[1] 1. Herstein, I. N., Noncommutative rings, Caru. Math. Monograph. 15, 1968. Google Scholar

[2] 2. Hoechsmann, K., Lifting ideals in noncommutative integral extensions, Canad. Math. Bull.(1) 13 (1970), 129-130. Google Scholar

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