I am reading the paper Lefschetz Properties and Hyperplane arrangements by E. Palezzato and M. Torielli,(https://arxiv.org/pdf/1911.04083.pdf) and I am having problems finding the definition of power-product of an element of a monomial ideal. Does someone have a reference for that?
Thanks in advance.
A power-product in a polynomial ring is just a product of powers of the variables. In $\mathbb{Q}[x, y]$ the power-products are $1,x,y,x^2,xy,y^2,x^3,x^2y,\ldots$. A non-zero polynomial is a sum of power-products with coefficients (see Definition 2.3).
The word 'monomial' is often used for the same concept, but some sources use the words (and words like 'term') differently, sometimes including coefficients.
For a reference, you will find it e.g. in all books dealing with Gröbner bases. As I mentioned, the terminology sometimes differs (but from Definition 2.3 it is clear what is meant in your case).