Zero ring
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This article is about the concept of a zero ring (indefinite article). For the zero ring (definite article), see trivial ring.
In ring theory, a branch of mathematics, a zero ring is a rng (a ring without unity) in which the product of any two elements is 0 (the additive neutral element).
A zero ring is commutative, and every subring is an ideal.
Each abelian group can be turned into a zero ring by defining the product of any two elements to be 0.
The concept of a zero ring should not be confused with the zero ring (also called the trivial ring), although the zero ring is a zero ring.
