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

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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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     title = {A {Remark} about {Noncommutative} {Integral} {Extensions}},
     journal = {Canadian mathematical bulletin},
     pages = {359--361},
     year = {1970},
     volume = {13},
     number = {3},
     doi = {10.4153/CMB-1970-067-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-067-0/}
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