# Ring:Z4

From Groupprops

## Definition

This ring, denoted or , is defined as the quotient of the ring of integers by the multiples of .

Note that the symbols and are *also* used for the additive group of this ring, which is the cyclic group of order four.

## Related groups

Group functor | Value | Explanation |
---|---|---|

additive group | cyclic group:Z4 | (4,1) |

multiplicative group | cyclic group:Z2 | (2,1) |

general linear group of degree two | general linear group:GL(2,Z4) | (96,195) |

special linear group of degree two | special linear group:SL(2,Z4) | (48,30) |

## GAP implementation

The ring can be defined using GAP's ZmodnZ function:

`ZmodnZ(4)`