Pseudo-ring
From AoPSWiki
A pseudo-ring is a ring that lacks a multiplicative identity. In other words, it is a set 
closed under two operations, addition and multiplication, such that 
is an abelian group, 
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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