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ON THE STANLEY DEPTH AND SIZE OF MONOMIAL IDEALS

Part of: Theory of modules and ideals Algebraic combinatorics

Published online by Cambridge University Press:  14 March 2017

S. A. SEYED FAKHARI
S. A. SEYED FAKHARI*
Affiliation:
School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran, and School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran e-mail: fakhari@khayam.ut.ac.ir
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Abstract

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Let $\mathbb{K}$ be a field and S = ${\mathbb{K}}$[x1, . . ., xn] be the polynomial ring in n variables over the field $\mathbb{K}$. For every monomial ideal I ⊂ S, we provide a recursive formula to determine a lower bound for the Stanley depth of S/I. We use this formula to prove the inequality sdepth(S/I) ≥ size(I) for a particular class of monomial ideals.

MSC classification

Primary: 13C15: Dimension theory, depth, related rings (catenary, etc.)
Secondary: 05E40: Combinatorial aspects of commutative algebra 13C13: Other special types
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 59 , Issue 3 , September 2017 , pp. 705 - 715
Copyright
Copyright © Glasgow Mathematical Journal Trust 2017 

References

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