The quotient ring $F_2[x,y]/(x,y)^2$ for the field $F_2$ of two elements.
Notes: Lattice of proper ideals is the diamond lattice. All ideals principal except for maximal ideal.
Keywords quotient ring
| Name | Measure | |
|---|---|---|
| cardinality | 8 | |
| composition length | left: 3 | right: 3 |
| Krull dimension (classical) | 0 |
| Name | Description |
|---|---|
| Idempotents | $\{0,1\}$ |
| Jacobson radical | Elements of "even weight" |
| Left singular ideal | Elements of "even weight" |
| Left socle | Elements of "even weight" |
| Nilpotents | Elements of "even weight" |
| Right singular ideal | Elements of "even weight" |
| Right socle | Elements of "even weight" |
| Unique maximal ideal | Elements of "even weight" |
| Units | Elements of "odd weight." |
| Zero divisors | Elements of "even weight" |