# Ring detail

## Name: Right-not-left coherent ring

Description: Let $s$ be a field endomorphism from $K$ to $K$ such that the image $L$ has infinite index in $K$. Define multiplication on $R=K\times K$ by $(x,y)(x',y')=(xx',s(x)y'+yx')$. $R$ is the ring

Keywords triangular ring

Reference(s):

• T.-Y. Lam. A first course in noncommutative rings. (2013) @ p 139

Legend
• = has the property
• = does not have the property
• = information not in database
Name Measure
Krull dimension (classical) 0
Name Description
Idempotents $\{0,1\}$