English

When is there a unique socle-vector associated to a given $h$-vector?

Commutative Algebra 2007-05-23 v2

Abstract

First, we construct a bijection between the set of hh-vectors and the set of socle-vectors of artinian algebras. As a corollary, we find the minimum codimension that an artinian algebra with a given socle-vector can have. Then, we study the main problem in the paper: determining when there is a unique socle-vector for a given hh-vector. We solve the problem completely if the codimension is at most 3.

Cite

@article{arxiv.math/0411229,
  title  = {When is there a unique socle-vector associated to a given $h$-vector?},
  author = {Fabrizio Zanello},
  journal= {arXiv preprint arXiv:math/0411229},
  year   = {2007}
}

Comments

21 pages; to appear in Comm. in Algebra