# Poset Embeddings of Hilbert functions and Betti numbers

```@article{Caviglia2012PosetEO,
title={Poset Embeddings of Hilbert functions and Betti numbers},
author={G. Caviglia and M. Kummini},
journal={arXiv: Commutative Algebra},
year={2012}
}```
• Published 2012
• Mathematics
• arXiv: Commutative Algebra
• We study inequalities between graded Betti numbers of ideals in a standard graded algebra over a field and their images under embedding maps, defined earlier by us in [Math. Z. 274, (2013), no. 3-4, pp. 809-819; arXiv:1009.4488]. We show that if graded Betti numbers do not decrease when we replace ideals in an algebra by their embedded versions, then the same behaviour is carried over to ring extensions. As a corollary we give alternative inductive proofs of earlier results of Bigatti, Hulett… CONTINUE READING
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