TY - JOUR
AU - Lu, Dancheng
PY - 2023/06/05
Y2 - 2024/08/04
TI - Linear resolutions and quasi-linearity of monomial ideals
JF - MATHEMATICA SCANDINAVICA
JA - Math. Scand.
VL - 129
IS - 2
SE - Articles
DO - 10.7146/math.scand.a-136634
UR - https://www.mscand.dk/article/view/136634
SP -
AB - <p>We introduce the notion of quasi-linearity and prove it is necessary for a monomial ideal to have a linear resolution and clarify all the quasi-linear monomial ideals generated in degree $2$. We also introduce the notion of a strongly linear monomial over a monomial ideal and prove that if $\mathbf {u}$ is a monomial strongly linear over $I$ then $I$ has a linear resolution (respectively is quasi-linear) if and only if $I+\mathbf {u}\mathfrak {p}$ has a linear resolution (respectively is quasi-linear). Here $\mathfrak {p}$ is any monomial prime ideal.</p>
ER -