Tensor product of modules: Difference between revisions

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==Balanced product==

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For a ring ''R'', a right ''R''-module ''M'', a left ''R''-module ''N'', and an abelian group ''G'', a map {{math|''φ'': ''M'' × ''N'' → ''G''}} is said to be '''''R''-balanced''', '''''R''-middle-linear''' or an '''''R''-balanced product''' if for all ''m'', ''m''′ in ''M'', ''n'', ''n''′ in ''N'', and ''r'' in ''R'' the following hold:{{refn|{{citation |author=Nathan Jacobson |title=Basic Algebra II |edition=2nd |year=2009 |publisher=[[Dover Publications]] }}}}{{rp|126}}