/sci/ - Science & Math

>>9014894
For example, [math]i=(1, 0, 0), j=(0, 1, 0), k=(0, 0, 1)[/math]. The first two are orthogonal, so let [math]a, b\in\mathbb{R}[/math] be arbitrary. Then you have [math]k\cdot(ai+bj)=0\cdot a+0\cdot b+1\cdot 0=0[/math].

>>9014897
Yeah, it's not. But, it shows there exists atleast one abelian group. Then pick its algebraic properties, and generalize. Then drop the abelianness part to generalize more. This would somehow seem like a logical way to continue after beginning with rings.