Zero ring

Builds on Ring

Example

The zero ring is the set $\{0\}$ with the operations $0 + 0 = 0$ and $0 \cdot 0 = 0$ . It is a commutative ring in which $1 = 0$ .

Remarks

A ring $R$ is the zero ring if and only if $1 = 0$ in $R$ . If $1 = 0$ , then $a = a \cdot 1 = a \cdot 0 = 0$ for each $a \in R$ . The zero ring is not an integral domain and not a field, because these definitions require $1 \neq 0$ .

Reading path

To understand this page from the ground up, read these 3 pages in order. The foundations come first.

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Group concept
Ring definition
Zero ring example

Tag	`008TBCYDPX`
URI	`m2://008TBCYDPX`
Aliases	`trivial-ring`
Kind	example
Writing	W2 usable
MSC	16B99
Instance of	Commutative ring
Uses	Ring
Same as	Wikidata Q1652969 Wikipedia Zero ring

Zero ring

Example

Remarks

Reading path

Further reading

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