Some recent results and open problems on sets of lengths of Krull monoids with finite class group

Wolfgang Schmid (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

Some of the fundamental notions related to sets of lengths of Krull monoids with finite class group are discussed, and a survey of recent results is given. These include the elasticity and related notions, the set of distances, and the structure theorem for sets of lengths. Several open problems are mentioned.

Mots clés: zero-sum sequences; sets of lengths; Krull monoids; maximal orders; minimal sets of distances; Davenport constant

Domaines: Algèbre commutative [math.AC]; Combinatoire [math.CO]; Théorie des nombres [math.NT]

Wolfgang Schmid. Some recent results and open problems on sets of lengths of Krull monoids with finite class group. Scott Chapman; Marco Fontana; Alfred Geroldinger; Bruce Olberding. Multiplicative Ideal Theory and Factorization Theory, 170, Springer International Publishing, pp.323-352, 2016, Springer Proceedings in Mathematics & Statistics, ⟨10.1007/978-3-319-38855-7_14⟩. ⟨hal-01233263⟩