Journal of Commutative Algebra

Acyclic digraphs giving rise to complete intersections

Walter D. Morris, Jr

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We call a directed acyclic graph a CI-digraph if a certain affine semigroup ring defined by it is a complete intersection. We show that if $D$ is a 2-connected CI-digraph with cycle space of dimension at least 2, then it can be decomposed into two subdigraphs, one of which can be taken to have only one cycle, that are CI-digraphs and are glued together on a directed path. If the arcs of the digraph are the covering relations of a poset, this is the converse of a theorem of Boussicault, Feray, Lascoux and Reiner. The decomposition result shows that CI-digraphs can be easily recognized.

Article information

J. Commut. Algebra, Volume 11, Number 2 (2019), 241-264.

First available in Project Euclid: 24 June 2019

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Primary: 14M10: Complete intersections [See also 13C40]
Secondary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65] 05C20: Directed graphs (digraphs), tournaments

Complete intersection cycle basis directed graph


Jr, Walter D. Morris,. Acyclic digraphs giving rise to complete intersections. J. Commut. Algebra 11 (2019), no. 2, 241--264. doi:10.1216/JCA-2019-11-2-241.

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