Ring $R_{ 81 }$

Bergman's unit-regular ring


See the expanded details page for the construction.

Notes: Given as an example of a unit-regular ring which contains a regular subring which isn't unit-regular.

Expanded details page.

Keywords endomorphism ring infinite matrix ring subring


  • K. C. O’Meara. A new setting for constructing von Neumann regular rings. (2017) @ Section 1
  • K. R. Goodearl. Von Neumann regular rings. (1991) @ Example 5.12, p 54
  • P. P. Nielsen and J. Ster. Connections between unit-regularity, regularity, cleanness, and strong cleanness of elements and rings. (2015) @ Section 2

  • = has the property
  • = does not have the property
  • = information not in database
Name Measure
composition length left: $\infty$right: $\infty$
weak global dimension 0
Name Description
Jacobson radical $\{0\}$
Left singular ideal $\{0\}$
Right singular ideal $\{0\}$