3 ms·
You may want to start here: https://en.wikipedia.org/wiki/Group_homomorphism https://en.wikipedia.org/wiki/Group_homomorphism The way I've understood it is th
by dvanduzer 12y ago
You may want to start here:
https://en.wikipedia.org/wiki/Group_homomorphism https://en.wikipedia.org/wiki/Group_homomorphism
The way I've understood it is that only addition has been possible so far. With a multiplication operation, you can get a field, and do "everything" with the real/complex numbers.
- darkxanthos 12y agoWell a homomorphism applies to a group and a group can only have one operator by definition. That won't change probably. Rings have two operators, fields are rings that support cancellation and integral fields I believe support inverses as a rule and where you'd get "everything" I believe.
- wging 12y ago"Well a homomorphism applies to a group" Not so. The notion's far more general: https://en.wikipedia.org/wiki/Ring_homomorphism https://en.wikipedia.org/wiki/Ring_homomorphism This gives us a notion of homomorphisms between fields. https://en.wikipedia.org/wiki/Homomorphism https://en.wikipedia.org/wiki/Homomorphism for more general notions of homomorphisms.
- darkxanthos 12y agoYou're right. My bad. Thanks for correcting me.