Homotopy, the codimension 2 correspondence and sections and rank 2 vector bundles (Q1902105)

In this paper, the author continues the study of certain addition and subtraction principles initiated by the reviewer [Comment. Math. Helv. 59, 243-252 (1984; Zbl 0559.13002)]. What the reviewer had proved for affine algebras over an algebraically closed field, the author generalises to a large extent to arbitrary Noetherian rings. For rings of dimension at least three, this was done by the author in an earlier paper [J. Algebra 176, No. 3, 947-958 (1995; Zbl 0849.13005)]. Here he deals with the case of dimension two rings. He proves the addition principle in its complete generality at least when the ideals in question are intersections of maximal ideals and the subtraction principle with some restriction. I will quote below just the addition principle to give a flavour of the results. Let \(A\) be a Noetherian ring with \(\dim A=2\). Let \(I_1\), \(I_2\) be two comaximal ideals of height 2 in \(A\), which are both intersections of finitely many maximal ideals. Suppose that both \(I_1\) and \(I_2\) are generated by two elements. Then so is \(I_1 \cap I_2\).