Difference between revisions of "Magma"
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| − | A '''magma''' (or a '''groupoid''') is a [[set]] <math> | + | A '''magma''' (or a '''groupoid''') is a [[set]] <math>S </math>, together with a function <math> \bot : S \times S \mapsto S </math>, i.e., a set with a [[binary operation]] <math> \bot </math>. A set <math>S </math> with an operation <math> \bot </math> that maps some proper [[subset]] of <math> S \times S </math> into <math>S </math> may be described as a magma with an operation ''not everywhere defined'' on <math>S </math>. |
Magmas so general that usually one studies special cases of magmas. For example, [[monoid]]s are [[associative]] magmas with an identity. | Magmas so general that usually one studies special cases of magmas. For example, [[monoid]]s are [[associative]] magmas with an identity. | ||
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{{stub}} | {{stub}} | ||
| + | [[Category:Mathematics]] | ||
Latest revision as of 18:34, 28 September 2024
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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