High Quality Content by WIKIPEDIA articles! In ring theory, a branch of mathematics, a zero ring is a ring (without unity) in which the product of any two elements is 0 (the additive identity element). (Note: Some authors define a zero ring to be a ring with a single element, see trivial ring. For a ring with unity a zero ring must be trivial.) Any abelian group can be turned into a zero ring by defining the product of any two elements to be 0. This proves that any abelian group is the additive group of some ring. Any subgroup of the additive group of a zero ring is an ideal. It follows that the only zero rings that are simple are those whose additive groups are cyclic groups of prime order.

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