Finitely Stable Domains and the Archimedean Property
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Researchers |
Muntasser Zahlan; Dr. Yousef Alwadi and Dr. Shawki Al Rashed |
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Published in |
Al-Baath Magazine for Applied Sciences, Volume 41, Issue 11, June 2019. |
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Abstract |
We study in this paper some properties of the Archimedean quadratic domains and the Archimedean finitely stable domains with stable maximal ideals, where we show that if R is an Archimedean quadratic domain and the domain R¥ is local, then dimR = 1. Also we show that Spec(R) is a totally ordered set for an Archimedean finitely stable local domain with stable maximal ideal, and each maximal ideal of the integral closure R̄ is a radical of principle ideal. Also we show that R is treed if R is a locally Archimedean stable domain with stable maximal ideals. Key words: fractional ideal, invertible ideal, stable ideal, Archimedean property. |
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Link to read full paper |
