Ring:Z4

This article is about a particular ring, i.e., a ring unique up to isomorphism. View a complete list of particular rings

Definition

This ring, denoted ${\mathbb{Z}}_4$ or $\mathbb{Z}/4\mathbb{Z}$, is defined as the quotient of the ring of integers by the multiples of $4$.

Note that the symbols ${\mathbb{Z}}_4$ and $\mathbb{Z}/4\mathbb{Z}$ 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)