Editing Polynomial ring (section)

=== Modules ===

The [[structure theorem for finitely generated modules over a principal ideal domain]] applies to
''K''[''X''], when ''K'' is a field. This means that every finitely generated module over ''K''[''X''] may be decomposed into a [[direct sum]] of a [[free module]] and finitely many modules of the form <math>K[X]/\left\langle P^k \right\rangle</math>, where ''P'' is an [[irreducible polynomial]] over ''K'' and ''k'' a positive integer.