Elsevier

Journal of Algebra

Volume 318, Issue 2, 15 December 2007, Pages 1027-1031
Journal of Algebra

Stanley conjecture in small embedding dimension

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Abstract

We show that Stanley's conjecture holds for a polynomial ring over a field in four variables. In the case of polynomial ring in five variables, we prove that the monomial ideals with all associated primes of height two, are Stanley ideals.

Keywords

Monomial ideals
Prime filtrations
Pretty clean filtrations
Stanley ideals

Cited by (0)

The authors are highly grateful to the School of Mathematical Sciences, GC University, Lahore, Pakistan in supporting and facilitating this research. The second author was supported by CNCSIS and the Contract 2-CEX06-11-20/2006 of the Romanian Ministery of Education and Research and the Higher Education Comission of Pakistan.