The zero module over a ring consists of a single zero element 0, with addition given by

and multiplication by any element of given by

The set is closed under both module operations. It also deserves the name trivial module, since it is the simplest module possible.

See also

Module, Singleton Set, Trivial, Trivial Ring, Zero Object

This entry contributed by Margherita Barile

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Cite this as:

Weisstein, Eric W., with contributions by Margherita Barile. "Zero Module." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ZeroModule.html

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