Brauer groups and class groups for Krull domains: a \(K\)-theoretic approach (Q1057941)

In this paper we prove that the exact sequence \[ 0\rightarrow\text{Pic}(R)\rightarrow \text{Cl}(R)\rightarrow \text{Bcl}(R)\rightarrow (R)\rightarrow \beta (R) \] defined by \textit{B. Auslander} [J. Algebra 4, 220--273 (1966; Zbl 0144.03401)], \textit{M. Orzech} [in: Brauer groups in ring theory and algebraic geometry, Proc., Antwerp 1981, Lect. Notes Math. 917, 66--90 (1982; Zbl 0492.13003)], and \textit{H. Lee} and \textit{M. Orzech} [Can. J. Math. 34, 996--1010 (1982; Zbl 0502.13004)] for a Krull domain \(R\) may be recovered as the \((K_ 0\), \(K_ 1)\)-exact sequence for some suitable category with product \(C(R)\).