The dimension of tensor products of AF-rings (Q2785923)

A commutative \(k\)-algebra \(A\) is an AF-ring if the height of \(P\) plus the transcendental dimension (t.d.) of \((A/P : k)\) equals t.d.\((A_P :k)\) for each prime ideal \(P\) of \(A\). -- \textit{A. R. Wadsworth} proved that if \(D_1\) and \(D_2\) are AF-domains, then NEWLINE\[NEWLINE\dim (D_1{\otimes}_k D_2)= \min\{\dim D_1+\text{t.d.}(D_1:k)\}, \text{t.d.}(D_1 :k)+\dim D_2\}.NEWLINE\]NEWLINE The authors, in this paper, extend many results in AF-domains to the class of AF-rings. They point out that the results do not extend trivially from domains to rings with zero divisors.NEWLINENEWLINEFor the entire collection see [Zbl 0855.00015].