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Elasticity of A+XI[X] domains where A is a UFD

✍ Scribed by Nathalie Gonzalez; Sébastien Pellerin; Richard Robert

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
120 KB
Volume
160
Category
Article
ISSN
0022-4049

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✦ Synopsis

Let A be a UFD and I be an ideal of A. We study the elasticity of atomic domains of the form A+XI [X ]. We prove this elasticity to be ÿnite if and only if I is a product of incomparable prime ideals where at most one of them is nonprincipal, then we provide an explicit computation in the ÿnite case.

📜 SIMILAR VOLUMES

Elasticity of A+XI[X] domains where A is
Elasticity of A+XI[X] domains where A is a Dedekind domain
✍ Sébastien Pellerin; Richard Robert 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 175 KB

Let A be a Dedekind domain and I be an ideal of A. We investigate the elasticity of integral domains of the form R = A + XI [X ]. Namely, when the ideal class group of A is inÿnite, we show that the elasticity of R is inÿnite, and when this group is ÿnite, we bound from below and above the elasticit