Geodesic
On the Product of Ideals
Canadian mathematical bulletin, Tome 26 (1983) no. 1, pp. 106-114

Voir la notice de l'article provenant de la source Cambridge University Press

This article introduces the concept of a condensed domain, that is, an integral domain R for which IJ = {ij: i ∊ I, j ∊ J} for all ideals I and J of R. This concept is used to characterize Bézout domains (resp., principal ideal domains; resp., valuation domains) in suitably larger classes of integral domains. The main technical results state that a condensed domain has trivial Picard group and, if quasilocal, has depth at most 1. Special attention is paid to the Noetherian case and related examples.
DOI : 10.4153/CMB-1983-016-2
Mots-clés : 13F05, 13A15, 13CT5, 13E05, 13G05 
Anderson, David F.; Dobbs, David E. On the Product of Ideals. Canadian mathematical bulletin, Tome 26 (1983) no. 1, pp. 106-114. doi: 10.4153/CMB-1983-016-2
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