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Factorization properties of Krull monoids with infinite class group

Wolfgang Hassler (2002)

Colloquium Mathematicae

For a non-unit a of an atomic monoid H we call L H ( a ) = k | a = u . . . u k w i t h i r r e d u c i b l e u i 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.

Non-embeddable 1 -convex manifolds

Jan Stevens (2014)

Annales de l’institut Fourier

We show that every small resolution of a 3-dimensional terminal hypersurface singularity can occur on a non-embeddable 1 -convex manifold.We give an explicit example of a non-embeddable manifold containing an irreducible exceptional rational curve with normal bundle of type ( 1 , - 3 ) . To this end we study small resolutions of c D 4 -singularities.

On domains with ACC on invertible ideals

Stefania Gabelli (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

If A is a domain with the ascending chain condition on (integral) invertible ideals, then the group I ( A ) of its invertible ideals is generated by the set I m ( A ) of maximal invertible ideals. In this note we study some properties of I m ( A ) and we prove that, if I ( A ) is a free group on I m ( A ) , then A is a locally factorial Krull domain.

Rational functions without poles in a compact set

W. Kucharz (2006)

Colloquium Mathematicae

Let X be an irreducible nonsingular complex algebraic set and let K be a compact subset of X. We study algebraic properties of the ring of rational functions on X without poles in K. We give simple necessary conditions for this ring to be a regular ring or a unique factorization domain.

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