Abstract Algebra: Theory and Applications · Problem 18.4.2

Lattices and Boolean Algebras — Thomas Judson

Mathematics — Abstract Algebra · gaussian-integers-factorization

Problem

The Gaussian integers,

\mathbb{Z}[i]

, are a UFD. Factor each of the following elements in

\mathbb{Z}[i]

into a product of irreducibles. ((a))

5

((b))

1 + 3i

((c))

6 + 8i

((d))

2

Hint. (a)

5 = -i(1+2i)(2+i)

; (c)

6+8i = -i(1+i)^2(2+i)^2