Direct product

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a direct product of objects already known can often be defined by giving a new one. That induces a structure on the <a href="/facts/Cartesian_product/BfqBWzdL">Cartesian product</a> of the underlying <a href="/facts/Set_(mathematics)/BfucfHMq">sets</a> from that of the contributing objects. More abstractly, the <a href="/facts/Product_(category_theory)/evFecz0t">product in category theory</a> is mentioned, which formalizes those notions.
Examples are the product of sets, <a href="/facts/Group_(mathematics)/IQTYqINt">groups</a> (described below), <a href="/facts/Product_ring/wBGSEE54">rings</a>, and other <a href="/facts/Algebraic_structures/TkuXca24">algebraic structures</a>. The <a href="/facts/Product_topology/0hg02IaX">product</a> of <a href="/facts/Topological_spaces/v2ut7CbK">topological spaces</a> is another instance.
There is also the <a href="/facts/Direct_sum/x3ljVsP6">direct sum</a>, which in some areas used interchangeably but in others is a different concept.

Direct product open-in-new

Direct product