<abstract xmlns="http://www.w3.org/1999/xhtml"> Let S be a polynomial algebra over a field. We study classes of monomial ideals (as for example lexsegment ideals) of S having minimal depth. In particular, Stanley's conjecture holds for these ideals. Also we show that if I is a monomial ideal with Ass(S/I) = {P1, P2, ..., Ps} and Pi ⊄ ∑s1=j≠i Pj for all i ∊ [s], then Stanley’s conjecture holds for S/I.</abstract>

Let S be a polynomial algebra over a field. We study classes of monomial ideals (as for example lexsegment ideals) of S having minimal depth. In particular, Stanley's conjecture holds for these ideals. Also we show that if I is a monomial ideal with Ass(S/I) = {P1, P2, ..., Ps} and Pi ⊄ ∑s1=j≠i Pj for all i ∊ [s], then Stanley’s conjecture holds for S/I.

Monomial ideals of minimal depth

Department of Mathematics, School of Natural Sciences, National University of Sciences and Technology Islamabad, Sector, H-12, 44000 Islamabad, Pakistan

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

{"article-title":"Monomial ideals of minimal depth"}

Let S be a polynomial algebra over a field. We study classes of monomial ideals (as for example lexsegment ideals) of S having minimal depth. In particular,...

Monomial ideals of minimal depth

Published Online: Mar 05, 2014

Page range: 147 - 154

DOI: https://doi.org/10.2478/auom-2013-0049

Keywords
Monomial ideal, Stanley decomposition, Stanley depth, Lexsegment ideal, Minimal depth

This content is open access.

Monomial ideals of minimal depth

Published Online: Mar 05, 2014

Page range: 147 - 154

DOI: https://doi.org/10.2478/auom-2013-0049

KeywordsMonomial ideal, Stanley decomposition, Stanley depth, Lexsegment ideal, Minimal depth

This content is open access.

Keywords
Monomial ideal, Stanley decomposition, Stanley depth, Lexsegment ideal, Minimal depth