Zero module

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 $R$ 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 $R$ is a ring, then every zero module is an initial object and a terminal object in the category of left $R$-modules.

This article is a stub. Help us out by expanding it.

See also

Invalid username
Login to AoPS