# Ring detail

## Name: Šter's clean ring with non-clean corner rings

Description: 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

Reference(s):

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

Legend
• = has the property
• = does not have the property
• = information not in database

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