Ring $R_{ 189 }$

Description:

Let $X$ be an uncountable set (specifically, we take a set of cardinality continuum) and $F(X)$ be the collection of all nonempty finite subsets of $X$. Construct the directed graph $G$ whose vertex set is $F(X)$, and there is an edge from $s_1$ to $s_2$ if and only if $s_1 \subsetneq s_2$. Take $L(G)$ to be the (non-unital) Leavitt path $\Bbb Q$-algebra on $G$. The ring is the Dorroh extension of $L(G)$ as a $\Bbb Q$-algebra: $D(\mathbb Q, L(G))$

Keywords Dorroh extension Leavitt path algebra