On positive affine monoids
2011 (English)In: Journal of Commutative Algebra, ISSN 1939-0807, Vol. 3, no 4, 511-536 p.Article in journal (Refereed) Published
For numerical monoids S the length of the k[S]-module k[(S) over bar]/k[S] is always finite. This is of course because the set of holes H(S) is finite, a property that does not hold in general for positive affine monoids of higher rank. We examine here in a combinatorial fashion positive affine monoids S with H(S) finite, or equivalently, positive affine monoids for which the length of k[(S) over bar]/k[S] is finite. This class of monoids turns out to behave in some respects like numerical monoids. In particular we describe the maximal elements in certain posets whose elements are positive affine monoids. Thus description provides natural higher dimensional versions of familiar classes of numerical monoids such as the class of symmetric numerical monoids.
Place, publisher, year, edition, pages
2011. Vol. 3, no 4, 511-536 p.
IdentifiersURN: urn:nbn:se:su:diva-81304DOI: 10.1216/JCA-2011-3-4-511ISI: 000307648100004OAI: oai:DiVA.org:su-81304DiVA: diva2:561543