Zero Module

Every module over a ring R contains a so-called "zero element" which fulfils the properties suggested by its name with respect to addition,

and with respect to multiplication by any element a of R,

This shows that the set {0} is closed under both module operations, and, therefore, it itself is a module, called the zero module. It also deserves the name trivial module, since it is the simplest module possible.

See also

This entry contributed by Margherita Barile

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

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