Wed Jan 24

(2-sided) ideals are exactly the kernels of ring homomorphisms.

The "multiplicative group" functor Ring -> Grp. Note that this only makes sense if ring homomorphisms are required to preserve the unit.

3 defs of G-set:
1. functor from C_G to Set
2. action map G x X -> X satisfying some properties
3. group homomorphism G -> Sym(X).

3 defs of left R-module:
1. additive functor from C_R to Ab
2. action map R x M -> M satisfying some properties
3. ring homomorphism R -> End(M).

Examples of modules. Sections of the Mobius bundle over the circle.