= Irreducible element of a commutative monoid
{title2=$a=bc\Longrightarrow b\in M^\times\ \text{or}\ c\in M^\times$}
= Irreducible elements of a commutative monoid
{synonym}
A nonunit element of a <commutative monoid> is irreducible if each factorization has a unit factor. In a submonoid of the positive integers under multiplication, the only unit is one. Irreducibility is relative to the allowed factors: a composite integer can be irreducible in a smaller monoid even though it is not a <prime number>.
Back to article page
