Change search
ReferencesLink to record
Permanent link

Direct link
On zanello's lower bound for level algebras
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2013 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 141, no 5, 1519-1527 p.Article in journal (Refereed) Published
Abstract [en]

We consider the proof of Söderberg of Zanello's lower bound for the Hilbert function of level algebras from the point of view of vector spaces. Our results, when specialised to level algebras, generalise those of Zanello and Söderberg to the case when the modules involved may have nontrivial annihilators. In the process we clarify why the methods of Zanello and Söderberg consist of two distinct parts. As a contrast we show that for polynomial rings, Zanello's bound, in the generic case, can be obtained by simple manipulations of numbers without dividing into two separate cases. We also consider the inclusion-exclusion principle of dimensions of vector spaces used by Zanello in special cases. It turns out that the resulting alternating sums are extremely difficult to handle and have many unexpected properties. This we illustrate by a couple of results and examples. The examples show that the inclusion-exclusion principle does not hold for vector spaces in the way it is used by Zanello.

Place, publisher, year, edition, pages
2013. Vol. 141, no 5, 1519-1527 p.
Keyword [en]
Graded modules, Hilbert functions, Inclusion-exclusion, Level algebras
National Category
URN: urn:nbn:se:kth:diva-127200DOI: 10.1090/S0002-9939-2012-11427-3ISI: 000326522400005ScopusID: 2-s2.0-84874197098OAI: diva2:643846

QC 20130828

Available from: 2013-08-28 Created: 2013-08-28 Last updated: 2013-11-29Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Search in DiVA

By author/editor
Laksov, Dan
By organisation
Mathematics (Dept.)
In the same journal
Proceedings of the American Mathematical Society

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 33 hits
ReferencesLink to record
Permanent link

Direct link