section_path: Properties/Multiplication
section_name: Multiplication
paragraph_text: Multiplication
  
  Analogously, given that addition has been defined, a multiplication operator × {\displaystyle \times } can be defined via a × 0 = 0 and a × S(b) = (a × b) + a. This turns (N ∗, ×) {\displaystyle (\mathbb {N} ^{*},\times)} into a free commutative monoid with identity element 1; a generator set for this monoid is the set of prime numbers.