Idempotent Elements for Integer Multiplication

From ProofWiki
Jump to navigation Jump to search


There are exactly two integers which are idempotent with respect to multiplication:

$0 \times 0 = 0$
$1 \times 1 = 1$


The integers $\struct {\Z, +, \times}$ form an integral domain.

By definition of integral domain, therefore, the integers form a ring with no (proper) zero divisors.

The result follows from Idempotent Elements of Ring with No Proper Zero Divisors.