Sequentially Cohen-Macaulay monomial ideals of embedding dimension four

Sarfraz Ahmad; Dorin Popescu

Sequentially Cohen-Macaulay monomial ideals of embedding dimension four

Commutative Algebra 2007-05-23 v2

Authors: Sarfraz Ahmad , Dorin Popescu

Abstract

Let $I$ be a monomial ideal of the polynomial ring $S=K[x_1,...,x_4]$ over a field $K$ . Then $S/I$ is sequentially Cohen-Macaulay if and only if $S/I$ is pretty clean. In particular, if $S/I$ is sequentially Cohen-Macaulay then $I$ is a Stanley ideal.

Keywords

cohen-macaulay rings and modules monomial ideals ideal theory

Cite

@article{arxiv.math/0702569,
  title  = {Sequentially Cohen-Macaulay monomial ideals of embedding dimension four},
  author = {Sarfraz Ahmad and Dorin Popescu},
  journal= {arXiv preprint arXiv:math/0702569},
  year   = {2007}
}

Comments

11 pages

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