🧩 A smaller part ➗ A math subset

submodule

9.8

In algebra, a smaller set inside a module that is closed under addition and multiplication by scalars

noun
/ˈsʌbˌmɒdʒuːl/

Specialized

: submódulo

The set of all even integers forms a submodule of the module of all integers.

Examples

Every submodule must be closed under both addition and scalar multiplication.
In the lecture, the professor explained how to identify a submodule within a given module.
The set of all even integers forms a submodule of the module of all integers.
A submodule must be closed under addition.
The mathematician defined a new submodule in her research.
In the lecture, the professor explained how to identify a submodule within a given module.
Every submodule must be closed under both addition and scalar multiplication.

Surface Forms

submodule singular

submodules plural

Morphology

submodule = module (transparent) = sub + module

In algebra the construction is regular: 'sub-' indicates a smaller or subordinate module within the larger module.

Etymology

Submodule is made of sub- and module, which helps explain its math meaning. Here sub- means 'smaller' like subway and module means 'a unit', so a mathematical submodule is a smaller set inside a module that itself behaves like a module and follows the same rules as the bigger one.