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Krull Domains of Generalized Power Series

✍ Scribed by Hwankoo Kim; Young Soo Park


Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
98 KB
Volume
237
Category
Article
ISSN
0021-8693

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✦ Synopsis


For an integral domain D and a torsion-free cancellative strictly subtotally Ε½ . ww S, F xx ordered monoid S, F , it is shown that the generalized power series ring D is a Krull domain if and only if D is a Krull domain and S is a Krull monoid.


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Euclidean-like Characterizations of Dede
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Though Euclidean domains are principal ideal domains, the converse is known to be false. We develop a notion like that of the Euclidean ring for which the converse is true. We similarly give new characterizations of Dedekind, Krull, and unique factorization domains. We also introduce the idea of ind