Change search
ReferencesLink to record
Permanent link

Direct link
On computer-assisted research in homological algebra
Stockholm University, Faculty of Science, Department of Mathematics. matematik.
1996 (English)In: Mathematics and Computers in Simulation, ISSN 0378-4754, Vol. 42, no 4-6, 475-490 p.Article in journal (Refereed) Published
Abstract [en]

We give a survey of how computer algebra can be used to help the mathematician to guess results and to prove theorems in homological algebra. Our main point is that the Poincaré-Betti series of a commutative graded algebra contains much deeper information and is harder to calculate than the Hilbert series of the same algebra. However, in many cases (going far beyond the so-called Koszul algebras), the two series are closely related, and this gives an interesting theory. This theory could hardly have been revealed without an intensive use of the programs MACAULAY by D. Bayer and M. Stillman and BERGMAN by J. Backelin. We also present new results and conjectures inspired by these studies and indicate how our results are related to problems in algebraic geometry and algebraic topology.

Place, publisher, year, edition, pages
1996. Vol. 42, no 4-6, 475-490 p.
Keyword [en]
Homological algebra, Macaulay, Bergman, Hilbert series, Poincaré-Betti series, Loop spaces
National Category
URN: urn:nbn:se:su:diva-13294OAI: diva2:179814
Available from: 2008-03-13 Created: 2008-03-13 Last updated: 2011-01-15Bibliographically approved

Open Access in DiVA

No full text

Other links

Search in DiVA

By author/editor
Roos, Jan-Erik
By organisation
Department of Mathematics

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

Total: 41 hits
ReferencesLink to record
Permanent link

Direct link