Linear resolutions and quasi-linearity of monomial ideals - Lu, Dancheng (MATHEMATICA SCANDINAVICA, 2023)
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 u is a monomial strongly linear over I then I has a linear resolution (respectively is quasi-linear) if and only if I+up has a linear resolution (respectively is quasi-linear). Here p is any monomial prime ideal.