A pseudo-ring is a ring that lacks a multiplicative identity. In other words, it is a set $R$ closed under two operations, addition and multiplication, such that $(R,+)$ is an abelian group, $(R,\cdot)$ is an associative magma, and multiplication is doubly distributive over addition.

By virtue of terrible pun, pseudo-rings are also called rngs (rings without i, the identity).

Ideals, divisors, and multiples may be defined as with rings.

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