## Algebra & Number Theory

### The semigroup of Betti diagrams

Daniel Erman

#### Abstract

The recent proof of the Boij–Söderberg conjectures reveals new structure about Betti diagrams of modules, giving a complete description of the cone of Betti diagrams. We begin to expand on this new structure by investigating the semigroup of such diagrams. We prove that this semigroup is finitely generated, and answer several other fundamental questions about it.

#### Article information

Source
Algebra Number Theory, Volume 3, Number 3 (2009), 341-365.

Dates
Revised: 22 January 2009
Accepted: 20 February 2009
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.ant/1513797403

Digital Object Identifier
doi:10.2140/ant.2009.3.341

Mathematical Reviews number (MathSciNet)
MR2525554

Zentralblatt MATH identifier
1173.13013

Subjects
Primary: 13D02: Syzygies, resolutions, complexes
Secondary: 13D25

#### Citation

Erman, Daniel. The semigroup of Betti diagrams. Algebra Number Theory 3 (2009), no. 3, 341--365. doi:10.2140/ant.2009.3.341. https://projecteuclid.org/euclid.ant/1513797403

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