Factorization properties of Krull monoids with infinite class group

Wolfgang Hassler

Colloquium Mathematicae, Tome 91 (2002), p. 229-242 / Harvested from The Polish Digital Mathematics Library

Résumé

For a non-unit a of an atomic monoid H we call $L_{H} (a) = k \in ℕ | a = u ₁ . . . u_{k} w i t h i r r e d u c i b l e u_{i} \in H$ the set of lengths of a. Let H be a Krull monoid with infinite divisor class group such that each divisor class is the sum of a bounded number of prime divisor classes of H. We investigate factorization properties of H and show that H has sets of lengths containing large gaps. Finally we apply this result to finitely generated algebras over perfect fields with infinite divisor class group.

Publié le : 2002-01-01

Zbl 0997.20056

EUDML-ID : urn:eudml:doc:285255

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     year = {2002},
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Wolfgang Hassler. Factorization properties of Krull monoids with infinite class group. Colloquium Mathematicae, Tome 91 (2002) pp. 229-242. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm92-2-7/