Ring $R_{ 119 }$

$\mathbb Q\langle x,y \rangle/(xy-1)$: the Toeplitz-Jacobson algebra


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)

  • = 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 $FM_\omega(\mathbb Q)$