Difference between revisions of "Zero module"
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Latest revision as of 09:12, 14 August 2009
A zero module is a module with one element, whose group structure is that of the trivial group, and whose ring acts trivially upon it. Technically speaking, for any ring there are infinitely many left zero modules, but they are trivially isomorphic, so by abuse of language we often refer to the zero module.
If is a ring, then every zero module is an initial object and a terminal object in the category of left -modules.
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