Ring $R_{ 67 }$

Šter's clean ring with non-clean corner rings


Construct $R_{70}$ as Šter describes using a field $F$ of characteristic $2$. Let $T$ be the subrng of $\omega\times\omega$ matrices over $R_{70}$ which have only finitely many nonzero entries. The ring $R=T+F\subseteq M_\omega(R_{70})$ is Šter's ring.

Keywords infinite matrix ring subring


  • J. Ster. Corner rings of a clean ring need not be clean. (2012) @ Example 3.4

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