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Koszulness, Krull dimension, and other properties of graph-related algebras

Constantinescu, Alexandru and Varbaro, Matteo. (2011) Koszulness, Krull dimension, and other properties of graph-related algebras. Journal of Algebraic Combinatorics, 34 (3). pp. 375-400.

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Official URL: http://edoc.unibas.ch/46500/

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Abstract

The algebra of basic covers of a graph G, denoted by A¯(G), was introduced by Herzog as a suitable quotient of the vertex cover algebra. In this paper we compute the Krull dimension of A¯(G) in terms of the combinatorics of G. As a consequence, we get new upper bounds on the arithmetical rank of monomial ideals of pure codimension 2. Furthermore, we show that if the graph is bipartite, then A¯(G) is a homogeneous algebra with straightening laws, and thus it is Koszul. Finally, we characterize the Cohen–Macaulay property and the Castelnuovo–Mumford regularity of the edge ideal of a certain class of graphs.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Ehemalige Einheiten Mathematik & Informatik > Algebra (Gorla)
UniBasel Contributors:Constantinescu, Alexandru
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Springer
ISSN:0925-9899
e-ISSN:1572-9192
Note:Publication type according to Uni Basel Research Database: Journal article -- The final publication is available at Springer see DOI link.
Language:English
Identification Number:
Last Modified:12 Jan 2017 10:37
Deposited On:12 Jan 2017 10:35

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