Properties of lexsegment ideals
Viviana Ene, Anda Olteanu, Loredana Sorrenti
TL;DR
This paper investigates the algebraic properties of lexsegment ideals, demonstrating conditions for linear quotients, regularity of the decomposition function, and characterizing Cohen-Macaulay cases, with explicit depth and dimension calculations.
Contribution
It establishes that lexsegment ideals with linear resolutions have linear quotients and regular decomposition functions, and provides a characterization of Cohen-Macaulay lexsegment ideals.
Findings
Lexsegment ideals with linear resolution have linear quotients.
The decomposition function is regular for completely lexsegment ideals with linear resolution.
The paper characterizes Cohen-Macaulay lexsegment ideals and computes their depth and dimension.
Abstract
We show that any lexsegment ideal with linear resolution has linear quotients with respect to a suitable ordering of its minimal monomial generators. For completely lexsegment ideals with linear resolution we show that the decomposition function is regular. For arbitrary lexsegment ideals we compute the depth and the dimension. As application we characterize the Cohen-Macaulay lexsegment ideals.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Cholinesterase and Neurodegenerative Diseases