3 ms·

Why is "commutative +" a step up rather than a step to the right? I guess there should be Abelian groups and commutative rings somewhere between groups and modu

Why is "commutative +" a step up rather than a step to the right? I guess there should be Abelian groups and commutative rings somewhere between groups and modules.

ivanbakel 7y ago
Probably because the diagram originated in a Vector Spaces book, and commutativity is viewed more as a valuable property than a structural constraint. Do physicists have any use for non-commutative algebra? It already seems pretty niche in mathematics.
- sergius 7y ago
  Rotation group maybe? And those gauge symmetries... heck, just look into quantum mechanics operators.
- QuesnayJr 7y ago
  All of quantum mechanics is non-commutative algebra. The commutative relation [x, p] = i*hbar gives you the Weyl algebra, for example.