[[Ring theory MOC]]
# Zero ring

The **zero ring** $0$ is the unique [[rng]] structure on the [[trivial group]] $\{ 0 \}$, #m/def/ring 
and is thus also a [[ring]].[^2009a]
It is [[Initial and terminal objects|initial and terminal]] in [[Category of rngs]],
while it is only terminal in [[Category of rings]],
since the codomain of a ring homomorphism from the zero ring must itself be the zero ring.[^2009b]

  [^2009a]: 2009\. [[@aluffiAlgebraChapter02009|Algebra: Chapter 0]], §III.1.2, p. 121
  [^2009b]: 2009\. [[@aluffiAlgebraChapter02009|Algebra: Chapter 0]], §III.2.1, p. 129

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