Journal article
t-linked extensions, the t-class group, and Nagata's theorem
Journal of pure and applied algebra, Vol.86(2), pp.109-124
1993
DOI: 10.1016/0022-4049(93)90097-D
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.
Details
- Title: Subtitle
- t-linked extensions, the t-class group, and Nagata's theorem
- Creators
- D. D AndersonEvan G HoustonMuhammad Zafrullah
- Resource Type
- Journal article
- Publication Details
- Journal of pure and applied algebra, Vol.86(2), pp.109-124
- DOI
- 10.1016/0022-4049(93)90097-D
- ISSN
- 0022-4049
- eISSN
- 1873-1376
- Language
- English
- Date published
- 1993
- Academic Unit
- Mathematics
- Record Identifier
- 9983985813802771
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