$k[x,y]/(x^2-y^3)$ where $k$ is a countably infinite field. Integral closure is $k[x/y]$.
Keywords polynomial ring quotient ring
Name | Measure | |
---|---|---|
cardinality | $\aleph_0$ | |
composition length | left: $\infty$ | right: $\infty$ |
Krull dimension (classical) | 1 |
Name | Description |
---|---|
Idempotents | $\{0,1\}$ |
Jacobson radical | $\{0\}$ |
Left singular ideal | $\{0\}$ |
Left socle | $\{0\}$ |
Nilpotents | $\{0\}$ |
Right singular ideal | $\{0\}$ |
Right socle | $\{0\}$ |
Zero divisors | $\{0\}$ |