Ring detail


Name: Bergman's unit-regular ring

Description: 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.

Krull dimension: (unknown)

Keywords endomorphism ring infinite matrix ring subring

Reference(s):

  • 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