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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