- branch of number theory
- use algebraic tools to study number-theoretic questions
- number-theoretic questions are expressed in terms of algebra, eg. how do we decompose an ideal?
- irreducible element: x is irreducible if x = ab then a or b is unit.
- prime: x is prime if x | ab then x | a or x | b
- fact: all elements of a notherian ring can be decomposed into irreducible elements