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t-linked extensions, the t-class group, and Nagata's theorem
Journal article   Open access   Peer reviewed

t-linked extensions, the t-class group, and Nagata's theorem

D. D Anderson, Evan G Houston and Muhammad Zafrullah
Journal of pure and applied algebra, Vol.86(2), pp.109-124
1993
DOI: 10.1016/0022-4049(93)90097-D
url
https://doi.org/10.1016/0022-4049(93)90097-DView
Published (Version of record) Open Access

Abstract

Let A be a subring of the integral domain B . Then B is said to be t-linked over A if for each finitely generated ideal I of A with I -1 = A , we have ( IB ) -1 = B . If A and B are Krull domains, this condition is equivalent to PDE. We show that if B is t-linked over A , then the map I →( IB ) t gives a homomorphism from the group of t-invertible t-ideals of A to the group of t-invertible t-ideals of B and hence a homomorphism Cl t ( A )→Cl t ( B ) of the t-class groups. Conditions are given for these maps to be surjective which extend Nagata's Theorem for Krull domains to a much larger class of domains including, e.g., Noetherian domains each of whose grade-one prime ideals has height one.

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