Elasticity of $A+XB[X]$ when $A\subset B$ is a minimal extension of integral domains
Volume 122 / 2011
Colloquium Mathematicum 122 (2011), 11-19
MSC: Primary 13A05, 13F15; Secondary 13A15, 13F20.
DOI: 10.4064/cm122-1-2
Abstract
We investigate the elasticity of atomic domains of the form $\Re =A+XB[X]$, where $X$ is an indeterminate, $A$ is a local domain that is not a field, and $A\subset B$ is a minimal extension of integral domains. We provide the exact value of the elasticity of $\Re $ in all cases depending the position of the maximal ideals of $B$. Then we investigate when such domains are half-factorial domains.
