Databases, Primality, and Category Theory

January 27, 2014

My fiancée is taking a databases course right now, and she pointed out that database normalization is related to prime factorization.

If we think of JOIN as a multiplication operation, and the multiplicative inverse as splitting a table into two tables, the equivalent process to prime factorization would be database normalization!

My limited background in abstract algebra and category theory makes me think this is a field, but do all fields have this property? Chemistry could possibly seen as a field with this property, where the prime factors would be the set of elements in a compound.