Pure Commutative Algebra

In the previous chapters, we mainly use Definition 1.5 and Lemma 1.1 , to compute several instances of Hadamard products of projective varieties. In order to do this, we used radical ideals associated to the varieties, but Definition 1.5 allows us to use different families of ideals, such as monomial ideals, square-free binomial ideals, and edge ideals. The possibility to use these different families of ideals opens up new and challenging research opportunities.