We study the freeness of the group Inv(D) of invertible ideals of an integral domain D, and the freeness of some related groups of (fractional) ideals. We study the relation between Inv(D) and Inv(DP), in particular in the locally finite case, and we analyze in more detail the case where D is Noetherian (obtaining a characterization of when Inv(D) is free for one-dimensional analytically unramified Noetherian domains) and where D is Prüfer.
Free groups of ideals
Spirito D.
2026-01-01
Abstract
We study the freeness of the group Inv(D) of invertible ideals of an integral domain D, and the freeness of some related groups of (fractional) ideals. We study the relation between Inv(D) and Inv(DP), in particular in the locally finite case, and we analyze in more detail the case where D is Noetherian (obtaining a characterization of when Inv(D) is free for one-dimensional analytically unramified Noetherian domains) and where D is Prüfer.File in questo prodotto:
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