Ring theory MOC Zero ring The zero ring is the unique rng structure on the trivial group , ring and is thus also a ring.1 It is 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.2 tidy | en | sembr Footnotes 2009. Algebra: Chapter 0, §III.1.2, p. 121 ↩ 2009. Algebra: Chapter 0, §III.2.1, p. 129 ↩