The ring is the quotient $\mathbb Q\langle x,y \rangle/(xy-1)$.

Notes: Minimum nonzero ideal is the left/right socle, generated by the $E_{i,j}$

Keywords free algebra quotient ring

- M. C. Iovanov and A. Sistko. On the Toeplitz-Jacobson algebra and direct finiteness. (2016) @ (whole article)
- T.-Y. Lam. A first course in noncommutative rings. (2013) @ Section 11 p 184
- V. Bavula. The algebra of one-sided inverses of a polynomial algebra. (2010) @ (whole article)

Symmetric properties

Asymmetric properties

Legend

- = has the property
- = does not have the property
- = information not in database

Name | Measure | |
---|---|---|

Krull dimension (classical) | 2 |

Name | Description |
---|---|

Jacobson radical | $\{0\}$ |

Left socle | $FM_\omega(\mathbb Q)$ |

Right socle | $FM_\omega(\mathbb Q)$ |