3 problems

Let $r\in\mathbb N_0$ and let $K$ be an arbitrary field. Let $\mathcal T$ be a maximal coclass tree in $\mathcal G_{r,K}$ with maximal infinite path $A_1\to A_2\to\cdots$. Write…

Let $r\in\mathbb N_0$ and let $K$ be an arbitrary field. For an algebra $A$ in $\mathcal G_{r,K}$, write $\mathcal T(A)$ for the rooted subgraph consisting of all paths starting at…

Let $r\in\mathbb N_0$ and let $K$ be an arbitrary field. The graph $\mathcal G_{r,K}$ has rooted-tree components, and a maximal infinite path is an infinite path starting at the ro…