Macaulay-Lex rings

Abed Abedelfatah

doi:10.1016/j.jalgebra.2012.10.025

Macaulay-Lex rings

Abed Abedelfatah

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We present simple proofs of Macaulay's theorem and Clements-Lindström's theorem. We generalize Shakin's theorem by proving that a stable ideal I of S is Macaulay-Lex if and only if I is a piecewise lexsegment ideal. We also study Macaulay-Lex ideals of the form 〈x1e1,x1t1x2e2,x1t1x2t2x3e3,..,x1t1〉xn-1tn-1xnen〉, where 2 ≤ _e1 ≤ ⋯ ≤ _{e n} ≤ ∞ and t _i < e _i for all i, and generalize Clements-Lindström's theorem.

Original language	English
Pages (from-to)	122-131
Number of pages	10
Journal	Journal of Algebra
Volume	374
DOIs	https://doi.org/10.1016/j.jalgebra.2012.10.025
State	Published - 5 Jan 2013
Externally published	Yes

Keywords

Hilbert function
Lex ideals
Macaulay-Lex ideals
Piecewise lexsegment ideals

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2012.10.025

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title = "Macaulay-Lex rings",

abstract = "We present simple proofs of Macaulay's theorem and Clements-Lindstr{\"o}m's theorem. We generalize Shakin's theorem by proving that a stable ideal I of S is Macaulay-Lex if and only if I is a piecewise lexsegment ideal. We also study Macaulay-Lex ideals of the form 〈x1e1,x1t1x2e2,x1t1x2t2x3e3,..,x1t1〉xn-1tn-1xnen〉, where 2 ≤ e1 ≤ ⋯ ≤ e n ≤ ∞ and t i < e i for all i, and generalize Clements-Lindstr{\"o}m's theorem.",

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doi = "10.1016/j.jalgebra.2012.10.025",

language = "English",

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T1 - Macaulay-Lex rings

AU - Abedelfatah, Abed

PY - 2013/1/5

Y1 - 2013/1/5

N2 - We present simple proofs of Macaulay's theorem and Clements-Lindström's theorem. We generalize Shakin's theorem by proving that a stable ideal I of S is Macaulay-Lex if and only if I is a piecewise lexsegment ideal. We also study Macaulay-Lex ideals of the form 〈x1e1,x1t1x2e2,x1t1x2t2x3e3,..,x1t1〉xn-1tn-1xnen〉, where 2 ≤ e1 ≤ ⋯ ≤ e n ≤ ∞ and t i < e i for all i, and generalize Clements-Lindström's theorem.

AB - We present simple proofs of Macaulay's theorem and Clements-Lindström's theorem. We generalize Shakin's theorem by proving that a stable ideal I of S is Macaulay-Lex if and only if I is a piecewise lexsegment ideal. We also study Macaulay-Lex ideals of the form 〈x1e1,x1t1x2e2,x1t1x2t2x3e3,..,x1t1〉xn-1tn-1xnen〉, where 2 ≤ e1 ≤ ⋯ ≤ e n ≤ ∞ and t i < e i for all i, and generalize Clements-Lindström's theorem.

KW - Hilbert function

KW - Lex ideals

KW - Macaulay-Lex ideals

KW - Piecewise lexsegment ideals

UR - https://www.scopus.com/pages/publications/84869050769

U2 - 10.1016/j.jalgebra.2012.10.025

DO - 10.1016/j.jalgebra.2012.10.025

M3 - Article

AN - SCOPUS:84869050769

SN - 0021-8693

VL - 374

SP - 122

EP - 131

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Macaulay-Lex rings

Abstract

Keywords

ASJC Scopus subject areas

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