Answer by user750041 for Why is there a hierarchy of interest between...
The definition of (abstract) group is historically patterned upon the properties of the bijections on a set: any three of them fulfill the associative property, but not every pair of them commute.
View ArticleAnswer by Noah Schweber for Why is there a hierarchy of interest between...
There absolutely are non-associative structures! Relevant terms here include "loop" and "Lie algebra." For concrete examples, consider octonion multiplication or the "midpoint" operation on points in...
View ArticleAnswer by Dietrich Burde for Why is there a hierarchy of interest between...
"Are there algebra structures which don't assume associativity ?" Yes, of course.See for example Lie algebras, Jordan algebras or more generally non-associative algebras. This includes also the...
View ArticleWhy is there a hierarchy of interest between associativity and commutativity
In mathematical structures, there are among other things : groups.Among their particular properties of the group, the groups have the property of associativity.Within the various groups, there are...
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