Ring:Z4

From Groupprops
Jump to: navigation, search

Template:Particular ring

Definition

This ring, denoted \Z_4 or \Z/4\Z, is defined as the quotient of the ring of integers by the multiples of 4.

Note that the symbols \Z_4 and \Z/4\Z 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)