Katzman, M. orcid.org/0000-0001-7553-3520 (1999) Bipartite graphs whose edge algebras are complete intersections. Journal of Algebra, 220 (2). pp. 519-530. ISSN 0021-8693
Abstract
Let R be monomial sub-algebra of $k[x_1,...,x_N]$ generated by square free monomials of degree two. This paper addresses the following question: when is R a complete intersection? For such a k-algebra we can associate a graph G whose vertices are $x_1,...,x_N$ and whose edges are $\{(x_i, x_j) | x_i x_j \in R \}$. Conversely, for any graph G with vertices $\{x_1,...,x_N\}$ we define the {\it edge algebra associated with G} as the sub-algebra of $k[x_1,...,x_N]$ generated by the monomials ${x_i x_j | (x_i,x_j) \text{is an edge of} G}$. We denote this monomial algebra by k[G]. This paper describes all bipartite graphs whose edge algebras are complete intersections.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 1999 Academic Press (Elsevier). This is an author produced version of a paper subsequently published in Journal of Algebra. Uploaded in accordance with the publisher's self-archiving policy. Article available under the terms of the CC-BY-NC-ND licence (https://creativecommons.org/licenses/by-nc-nd/4.0/) |
Keywords: | math.AC; math.AC; math.AG; 14M10 14M25 05E |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 27 Mar 2017 08:29 |
Last Modified: | 18 Jul 2017 23:34 |
Published Version: | http://www.sciencedirect.com/science/article/pii/S... |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:113497 |