# Ring detail

## Name: $F_2[x,y]/(x,y)^2$

Description: 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. Zero Krull dimension

Keywords quotient ring

Reference(s):

• (Citation needed)

• This ring has the following properties:
The ring lacks the following properties:
We don't know if the ring has or lacks the following properties: