Let $F = \Bbb Q$ and take an $F$-linear basis $S$ of $F(X)$ that contains the integer powers of $X$. Suppose $T$ is the free product of $F(X)$ with the two-generated free algebra $F\langle A,B \rangle$ over $F$. Let $w$ run through $S \setminus \{1\}$ and $q$ through $S \setminus \{X^{-i}: i > 0\}$; form the ideal $P \lhd T$ generated by $A^2, B^2, AwA, AwB, BwB, BqA$ and $\bigcup\limits_{k=1}^\infty \{B X^{-1} A, \ldots, B X^{-k} A\}^{n_k}$ for $n_k = 2^k + 2$. The ring is $T/P$.
(Nothing was retrieved.)
| Name | Description |
|---|---|
| Idempotents | $\{0,1\}$ |
| Jacobson radical | $(A, B)/P$ |
| Left socle | $\{0\}$ |
| Right socle | $\{0\}$ |