Abstract
In this paper, we extend the notion of quasi-linear quotients for a pure monomial ideal (not necessarily square-free) of degree d. We introduce the notion of quasi-linear free resolution and show that if a pure monomial ideal I = (u1, u2,…, um) of degree d in the polynomial ring S = k[x1,…, xn] admits quasi-linear quotients then Lq = (u1,…, uq−1): uq admits quasi-linear free resolution for all q ≤ m. Moreover, we show that if a pure monomial ideal I of degree d admits quasi-linear quotients then I〈t〉 will also have quasi-linear quotients for t ≥ d.
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Submitted by E. K. Lipachev
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Nazir, S., Anwar, I. & Ahmad, A. Monomial Ideals with Quasi-Linear Quotients. Lobachevskii J Math 40, 85–89 (2019). https://doi.org/10.1134/S1995080219010116
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DOI: https://doi.org/10.1134/S1995080219010116