It's all a generalization of Linear Algebra!

Linear Algebra: The study of vector spaces over fields.

Examples 0 R RxR RxRxR
Pictures R0 diagram R1 diagram R2 diagram R3 diagram
Generators
0
1
[1]  [0]
[0], [1]
[1]  [0]  [0]
[0], [1], [0]
[0]  [0]  [1]



Commutative Algebra: The study of modules over commutative rings.

Examples:


Question:

We know how to decompose a vector space into products and how to give generators for a vector space. What about modules?