Structure theorem for finitely generated modules over a principal ideal domain

<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, in the field of <a href="/facts/Abstract_algebra/YNNE1CNz">abstract algebra</a>, the structure theorem for finitely generated modules over a principal ideal domain is a generalization of the <a href="/facts/Fundamental_theorem_of_finitely_generated_abelian_groups/dwtl7mp4">fundamental theorem of finitely generated abelian groups</a> and roughly states that <a href="/facts/Finitely_generated_module/6Njcpgzr">finitely generated</a> <a href="/facts/Module_(mathematics)/jP0LIhFL">modules</a> over a <a href="/facts/Principal_ideal_domain/JCwAUnyW">principal ideal domain</a> (PID) can be uniquely decomposed in much the same way that <a href="/facts/Integer/PUwwrawx">integers</a> have a <a href="/facts/Prime_factorization/EjMCTz2t">prime factorization</a>.  The result provides a simple framework to understand various canonical form results for <a href="/facts/Square_matrix/5TP9mNNn">square matrices</a> over <a href="/facts/Field_(mathematics)/xAjAS4ko">fields</a>.
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Structure theorem for finitely generated modules over a principal ideal domain open-in-new

Structure theorem for finitely generated modules over a principal ideal domain