Seminar “Factorizations of polynomials with integral non-negative coefficients" (Zoom), Open Seminar - School of Mathematical Sciences, Hebei Normal University, China.

Factorizations of polynomials with integral non-negative coefficients Abstract: We study the structure of the commutative multiplicative monoid N0x∗ of all the non-zero polynomials in Zx with non-negative coefficients. We first recall some important tools for investigating non-unique factorizations in monoids (sets of lengths, elasticity, catenary degrees, etc.), and we show that N0x∗ is surprisingly very far from being factorial. Then, we describe prime elements and prime ideals of N0x∗, and we conclude with some open problems. The talk is based on joint work with Alberto Facchini.