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Almost factoriality of integral domains and Krull-like domains

โœ Scribed by Chang, Gyu Whan; Kim, Hwankoo; Lim, Jung Wook


Book ID
120066353
Publisher
Mathematical Sciences Publishers
Year
2012
Tongue
English
Weight
613 KB
Volume
260
Category
Article
ISSN
0030-8730

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๐Ÿ“œ SIMILAR VOLUMES


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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

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โœ Scott T. Chapman; Franz Halter-Koch; Ulrich Krause ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 207 KB

We investigate two classes of monoids and integral domains, called inside and outside factorial, whose definitions are closely related in a divisor-theoretic manner to the concept of unique factorization. We prove that a monoid is outside factorial if and only if it is a Krull monoid with torsion cl