Title : ( The strong persistence property and symbolic strong persistence property )
Authors: , Kazem Khashyarmanesh , Leslie G. Roberts , Jonathan Toledo ,
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Abstract
Let I be an ideal in a commutative Noetherian ring R. Then the ideal I has the strong persistence property if and only if (Ik+1 : RI) = Ik for all k, and I has the symbolic strong persistence property if and only if (I(k+1) : RI(1)) = I(k) for all k, where I(k)denotes the kth symbolic power of I. We study the strong persistence property for some classes of monomial ideals. In particular, we present a family of primary monomial ideals failing the strong persistence property. Finally, we show that every square-free monomial ideal has the symbolic strong persistence property
Keywords
strong persistence property; associated prime; cover ideal; symbolic strong persistence property
@article{paperid:1094214,
author = {, and Khashyarmanesh, Kazem and Leslie G. Roberts and Jonathan Toledo},
title = {The strong persistence property and symbolic strong persistence property},
journal = {Czechoslovak Mathematical Journal},
year = {2022},
volume = {72},
number = {1},
month = {April},
issn = {1572-9141},
pages = {209--237},
numpages = {28},
keywords = {strong persistence property; associated prime; cover ideal; symbolic strong
persistence property},
}
%0 Journal Article
%T The strong persistence property and symbolic strong persistence property
%A ,
%A Khashyarmanesh, Kazem
%A Leslie G. Roberts
%A Jonathan Toledo
%J Czechoslovak Mathematical Journal
%@ 1572-9141
%D 2022
