Magma
From AoPSWiki
A magma (or a groupoid) is a set 
, together with a function 
, i.e., a set with a binary operation 
. A set with an operation that maps some proper subset of 
into may be described as a magma with an operation not everywhere defined on .
Magmas so general that usually one studies special cases of magmas. For example, monoids are associative magmas with an identity.
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