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On the class group of a pullback

✍ Scribed by Saı̈d El Baghdadi

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
135 KB
Volume
169
Category
Article
ISSN
0022-4049

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✦ Synopsis

Let T be an integral domain, I a nonzero proper ideal of T , and ' : T → T=I the natural projection. For an integral domain D which is a proper subring of T=I , R = ' -1 (D) is then a subring of T . We investigate the class group Cl(R), the Picard group Pic(R), and the local class group G(R) of the pullback R.

📜 SIMILAR VOLUMES

On the Class Group and the Local Class G
On the Class Group and the Local Class Group of a Pullback
✍ Marco Fontana; Stefania Gabelli 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 335 KB

Partially supported by the research funds of Ministero dell'Uni¨ersita e della Ricerca Scientifica e Tecnologica and by Grant 9300856.CT01 of Consiglio Nazionale delle Ricerche.

On the class group of a graded domain
On the class group of a graded domain
✍ S. El Baghdadi; L. Izelgue; S. Kabbaj 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 130 KB

This paper studies the class group of a graded integral domain R = ∈ R . We prove that if the extension R0 ⊂ R is inert, then Cl(R) = HCl(R) if and only if R is almost normal. As an application, we state a decomposition theorem for class groups of semigroup rings, namely, Cl(A[ ]) ∼ = Cl(A) ⊕ HCl(K[