Abstract
We use initially regular sequences that consist of linear sums to explore the depth of \(R/I^2\), when I is a monomial ideal in a polynomial ring R. We give conditions under which these linear sums form regular or initially regular sequences on \(R/I^2\). We then obtain a criterion for when \({{\,\mathrm{depth}\,}}R/I^2>1\) and a lower bound on \({{\,\mathrm{depth}\,}}R/I^2\).
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The authors would like to thank the referees for the careful review of the article and for the suggestions that improved the article. The second author is partially supported by Simons Foundation and Louisiana Board of Regents.
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Communicated by Isidoro Gitler.
Dedicated to Rafael H. Villarreal on the occasion of his 70th birthday.
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Fouli, L., Hà, T.H. & Morey, S. Regular sequences on squares of monomial ideals. São Paulo J. Math. Sci. 17, 122–146 (2023). https://doi.org/10.1007/s40863-022-00337-5
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DOI: https://doi.org/10.1007/s40863-022-00337-5