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Elasticity Properties Preserved in the Normset

✍ Scribed by Jim Coykendall

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 76 KB
Volume: 94
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.2001.2740

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✦ Synopsis

Let T ı R be the rings of integers in a number field and a finite Galois extension field. We study relations between the elasticity r(R) of the monoid of nonzero elements of R and the elasticity r(S) of the monoid S of norms to T of those elements. We show r(R) \ r(S) and that equality holds if the norms of irreducible elements of R are irreducible in S, which is true, in particular, if either r(R) < 2 or r(S)=1.

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