On Nagata's pairwise algorithm
The author studies some properties of a commutative ring with a pairwise algorithm, a concept extending that of Euclidean algorithm introduced by \textit{M. Nagata} [in: Commutative Algebra and Combinatorics, US-Jap. joint Semin., Kyoto 1985, Adv. Stud. Pure Math. 11, 167-171 (1987; Zbl 0701.13008)]. For instance if \(E_1 = E_2 \oplus E_3\) where \(E_i\) are rings, then \(E\) has a pairwise algorithm if and only if \(E_2\) and \(E_3\) have a pairwise algorithm. If an integral domain \(E\) has a pairwise algorithm and \(S\) is a multiplicative subset not containing 0, then the ring of fractions \(S^{-1}E\) has a pairwise algorithm.
scientific article; zbMATH DE number 589935