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math.AC2023
On the arithmetic of ultraproducts of commutative cancellative monoids
Daniel Windisch
We develop first steps in the study of factorizations of elements in ultraproducts of commutative cancellative monoids into irreducible elements. A complete characterization of the…
math.AC2023
Lengths of factorizations of integer-valued polynomials on Krull domains with prime elements
Victor Fadinger, Daniel Windisch
Let be a Krull domain admitting a prime element with finite residue field and let be its quotient field. We show that for all positive integers and $1 < n_1 \leq \ldots…
math.AC2023
On local divisor class groups of complete intersections
Daniel Windisch
Samuel conjectured in 1961 that a (Noetherian) local complete intersection ring that is a UFD in codimension at most three is itself a UFD. It is said that Grothendieck invented lo…