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- Title
HIGHER-ORDER CLASS GROUPS AND BLOCK MONOIDS OF KRULL MONOIDS WITH TORSION CLASS GROUP.
- Authors
SCHMID, WOLFGANG A.
- Abstract
Extensions of the notion of a class group and a block monoid associated to a Krull monoid with torsion class group are introduced and investigated. Instead of assigning to a Krull monoid only one abelian group (the class group) and one monoid of zero-sum sequences (the block monoid), we assign to it a recursively defined family of abelian groups, the first being the class group, and do alike for the block monoid. These investigations are motivated by the aim of gaining a more detailed understanding of the arithmetic of Krull monoids, including Dedekind and Krull domains, both from a technical and conceptual point of view. To illustrate our method, some first arithmetical applications are presented.
- Subjects
MONOIDS; SEMIGROUPS (Algebra); TORSION; DEFORMATIONS (Mechanics); GROUP theory
- Publication
Journal of Algebra & Its Applications, 2010, Vol 9, Issue 3, p433
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498810004002