Geodesic
Elasticity of $A+XB[X]$ when $A\subset B$ is a minimal extension of integral domains
Ahmed Ayache 1   ; Hanen Monceur 2
1 Department of Mathematics Faculty of Science University of Sana'a P.O. Box 12460, Sana'a, Yemen
2 Department of Mathematics Faculty of Science University of Sfax P.O. Box 1171, 3000 Sfax, Tunisia
Colloquium Mathematicum, Tome 122 (2011) no. 1, pp. 11-19 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm122-1-2
Keywords: investigate elasticity atomic domains form where indeterminate local domain field subset minimal extension integral domains provide exact value elasticity cases depending position maximal ideals investigate domains half factorial domains

Ahmed Ayache  1   ; Hanen Monceur  2

1 Department of Mathematics Faculty of Science University of Sana'a P.O. Box 12460, Sana'a, Yemen
2 Department of Mathematics Faculty of Science University of Sfax P.O. Box 1171, 3000 Sfax, Tunisia 
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Ahmed Ayache; Hanen Monceur. Elasticity of $A+XB[X]$ when $A\subset B$ is a minimal extension of integral domains. Colloquium Mathematicum, Tome 122 (2011) no. 1, pp. 11-19. doi: 10.4064/cm122-1-2

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