Results on the normality of square-free monomial ideals and cover ideals under some graph operations - Al-Ayyoub, Ibrahim; Nasernejad, Mehrdad; Khashyarmanesh, Kazem; Roberts, Leslie G.; Quiñonez, Veronica Crispin (MATHEMATICA SCANDINAVICA, 2021)
In this paper, we introduce techniques for producing normal square-free monomial ideals from old such ideals. These techniques are then used to investigate the normality of cover ideals under some graph operations. Square-free monomial ideals that come out as linear combinations of two normal ideals are shown to be not necessarily normal; under such a case we investigate the integral closedness of all powers of these ideals.