1,022 research outputs found
Uniquely presented finitely generated commutative monoids
A finitely generated commutative monoid is uniquely presented if it has only
a minimal presentation. We give necessary and sufficient conditions for
finitely generated, combinatorially finite, cancellative, commutative monoids
to be uniquely presented. We use the concept of gluing to construct commutative
monoids with this property. Finally for some relevant families of numerical
semigroups we describe the elements that are uniquely presented.Comment: 13 pages, typos corrected, references update
Flatness Properties of Acts over Commutative, Cancellative Monoids
This note presents a classification of commutative, cancellative monoids S by flatness properties of their associated S-acts
Affine semigroups having a unique Betti element
We characterize affine semigroups having one Betti element and we compute
some relevant non-unique factorization invariants for these semigroups. As an
example, we particularize our description to numerical semigroups.Comment: 8 pages, 1 figure. To appear in Journal of Algebra and its
Application
Termination orders for 3-dimensional rewriting
This paper studies 3-polygraphs as a framework for rewriting on
two-dimensional words. A translation of term rewriting systems into
3-polygraphs with explicit resource management is given, and the respective
computational properties of each system are studied. Finally, a convergent
3-polygraph for the (commutative) theory of Z/2Z-vector spaces is given. In
order to prove these results, it is explained how to craft a class of
termination orders for 3-polygraphs.Comment: 30 pages, 35 figure
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