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Euclidean Rings

The cardinality of the set of units, and of the set of equivalence classes of primes in non-trivial Euclidean domains is discussed with reference to the categories "finite" and "infinite." It is shown that no Euclidean domains exist for which both of these sets are finite. The other three combinations are possible and examples are given. For the more general Euclidean rings, the first combination is possible and examples are likewise given. Prime factorization is also discussed in both Euclidean rings and Euclidean domains. For Euclidean rings, an alternative definition of prime elements in terms of associates is compared and contrasted to the usual definitions.

Identiferoai:union.ndltd.org:unt.edu/info:ark/67531/metadc663654
Date05 1900
CreatorsFecke, Ralph Michael
ContributorsBrewer, Burns W., Isaacson, Portia
PublisherNorth Texas State University
Source SetsUniversity of North Texas
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation
Formativ, 32 leaves, Text
RightsPublic, Fecke, Ralph Michael, Copyright, Copyright is held by the author, unless otherwise noted. All rights

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