Geometric and combinatorial aspects of submonoids of a finite-rank free commutative monoid. (English) Zbl 1458.20050
The author considers commutative, cancellative, reduced monoids \(M\) (written additively), which can be embedded into a finite-dimensional vector space \(V\) over an ordered field. This paper gives a nice overview how arithmetic properties of \(M\) (unique factorization, half-factorial, other-half-factorial, primary, finitary) correspond to geometric properties of the cone, which is generated by \(M\) inside \(V\).
Reviewer: Günter Lettl (Graz)
MSC:
| 20M14 | Commutative semigroups |
| 20M13 | Arithmetic theory of semigroups |
| 52A20 | Convex sets in \(n\) dimensions (including convex hypersurfaces) |
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