5 problems

Conway's conjecture. The series $1+\sum_n t^{-\frac{1}{n}}$ is irreducible in $\mathbb{Z}+\mathbb{R}((G^{<0}))$. Conway's conjecture was proved by Berarducci, so this statement is…

Let $K$ be a field, let $P_\alpha$ denote the principal series of order type $\omega^\alpha$, and let $R_\alpha$ denote the corresponding set of products of principal series appear…

Let $K$ be a field and let $b\in K((\mathbb{R}^{\leq 0}))$ be a random generalized power series, meaning that either $\operatorname{cl}(\operatorname{supp}(b))-\{0\}$ is…

Let $K((\mathbb{R}^{\leq 0}))$ be the ring of generalized power series, let $J$ be the germ ideal, and let $v_J$ denote the order-value. A series $a\in K((\mathbb{R}^{\leq 0}))$ is…

Let $K((\mathbb{R}^{\leq 0}))$ be the ring of generalized power series, let $J$ be the ideal defining germs, and consider the quotient ring $K((\mathbb{R}^{\leq 0}))/J$. Berarducci…