5 problems

Let $R$ be a local Noetherian domain, and let $Star(R)$ denote the set of star operations on $R$. A domain $R$ is star regular if $|Star(T)|\leq |Star(R)|$ for every overring $T$ o…

Let $\mathbf{s}$ be a sequence of pairs of positive integers with $n(\mathbf{s})=4$, and let $\Lambda(\mathbf{s},q)$ denote the number of star operations associated with…

Let $\mathbf{s}$ and $\mathbf{t}$ be sequences of pairs of positive integers, and let $n(\mathbf{s})$ and $n(\mathbf{t})$ be their associated integers. For each finite-field cardin…

Let $\mathbf{s}$ be a sequence of pairs of positive integers, and let $n(\mathbf{s})$ denote the associated integer appearing in the definition of $\theta(\mathbf{s},q)$. For a fin…

Let $D$ be a one-dimensional local Noetherian domain, let $K$ be its quotient field, and let $\mathrm{Star}(D)$ denote the set of star operations on $D$. The domain $D$ is star reg…