Elasticity of $A+XB[X]$ when $A\subset B$ is a minimal extension of integral domains

Ahmed Ayache; Hanen Monceur

doi:10.4064/cm122-1-2

Instytut Matematyczny Polskiej Akademii Nauk / Institute of Mathematics / Publishing house / Journals and Serials / Colloquium Mathematicum / All issues

Elasticity of $A+XB[X]$ when $A\subset B$ is a minimal extension of integral domains

Volume 122 / 2011

Ahmed Ayache, Hanen Monceur 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.

Authors

Ahmed AyacheDepartment of Mathematics
Faculty of Science
University of Sana'a
P.O. Box 12460, Sana'a, Yemen
e-mail
Hanen MonceurDepartment of Mathematics
Faculty of Science
University of Sfax
P.O. Box 1171, 3000 Sfax, Tunisia
e-mail

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Instytut Matematyczny Polskiej Akademii Nauk / Institute of Mathematics / Publishing house / Journals and Serials / Colloquium Mathematicum / All issues

Colloquium Mathematicum

Elasticity of A+XB[X] when A\subset BA\subset B is a minimal extension of integral domains

Volume 122 / 2011

Abstract

Authors

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Elasticity of $A+XB[X]$ when $A\subset B$ is a minimal extension of integral domains