Journal article
Splitting the t-class group
Journal of pure and applied algebra, Vol.74(1), pp.17-37
1991
DOI: 10.1016/0022-4049(91)90046-5
Abstract
Let D be an integral domain and S a saturated multiplicatively closed subset of D . We say that S is a splitting set if for each 0 ≠ d ϵ D , we can write d as the product d = sa , where s ϵ S and a ϵ D , with s ' D ∩ aD = s ' aD for all s ' ϵ S . An important example of a splitting set is the multiplicatively closed set generated by a set of principal primes having the property that for each 0 ≠ d ϵ D , there is a bound on the length of a product of these primes dividing d . If S is a splitting set, then T = {0 ≠ t ϵ D | tD ∩ sD = tsD for all s ϵ S } is a saturated multiplicatively closed subset of D . We show that the map from the monoid T ( D ) of t-ideals of D to the cardinal product T ( D S ) x c T ( D t ), given by A → ( AD S , AD T ), is an order-preservin g monoid isomorphism. Moreover, the induced map Cl t ( D ) → Cl t ( D S ) x Cl t ( D τ ), given by [ A ] → ([ AD S ], [ AD τ ]), is an isomorphism which splits the t-class group of D . Applications and examples of this splitting are given.
Details
- Title: Subtitle
- Splitting the t-class group
- Creators
- D. D AndersonDavid F AndersonMuhammad Zafrullah
- Resource Type
- Journal article
- Publication Details
- Journal of pure and applied algebra, Vol.74(1), pp.17-37
- DOI
- 10.1016/0022-4049(91)90046-5
- ISSN
- 0022-4049
- eISSN
- 1873-1376
- Language
- English
- Date published
- 1991
- Academic Unit
- Mathematics
- Record Identifier
- 9983985977202771
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