Abstract
Let Δ be a finite simplicial complex on the vertex set V = {x1,..., xn}. Recall that this means that Δ is a collection of subsets of V such that \( F \subseteq G \in \Delta \Rightarrow F \in \Delta {\mathbf{ }}{\text{and}}{\mathbf{ }}{\text{\{ }}x_1 {\text{\} }} \in \Delta {\mathbf{ }}{\text{for}}{\mathbf{ }}{\text{all}}{\mathbf{ }}x_i \in V. \) . The elements of Δ are called faces. If F ∈ Δ, then define dim F: = |F| − 1 and dim Δ: = maxF∈Δ(dim F). Let d = dim Δ + 1. Given any field k we now define the face ring (or Stanley-Reisner ring) k[Δ] of the complex Δ.
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© 1996 Birkhäuser Boston
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(1996). The Face Ring of a Simplicial Complex. In: Combinatorics and Commutative Algebra. Progress in Mathematics, vol 41. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4433-4_3
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DOI: https://doi.org/10.1007/0-8176-4433-4_3
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4369-0
Online ISBN: 978-0-8176-4433-8
eBook Packages: Springer Book Archive