@article{Lu_2023, title={Linear resolutions and quasi-linearity of monomial ideals}, volume={129}, url={https://www.mscand.dk/article/view/136634}, DOI={10.7146/math.scand.a-136634}, abstractNote={<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>}, number={2}, journal={MATHEMATICA SCANDINAVICA}, author={Lu, Dancheng}, year={2023}, month={Jun.} }