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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 ∈ ℕ | a = u ₁ . . . 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.

Flatness testing over singular bases

Janusz Adamus, Hadi Seyedinejad (2013)

Annales Polonici Mathematici

We show that non-flatness of a morphism φ:X→ Y of complex-analytic spaces with a locally irreducible target of dimension n manifests in the existence of vertical components in the n-fold fibred power of the pull-back of φ to the desingularization of Y. An algebraic analogue follows: Let R be a locally (analytically) irreducible finite type ℂ-algebra and an integral domain of Krull dimension n, and let S be a regular n-dimensional algebra of finite type over R (but not necessarily a finite R-module),...

Fully inert submodules of torsion-free modules over the ring of p-adic integers

B. Goldsmith, L. Salce, P. Zanardo (2014)

Colloquium Mathematicae

Fully inert submodules of torsion-free J p -modules are investigated. It is proved that if the module considered is either free or complete, these submodules are exactly those which are commensurable with fully invariant submodules; examples are given of torsion-free J p -modules for which this property fails.

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