module
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generalization of vector space, with scalars in a ring instead of a field
Wikidata facts
- Subclass of
- algebraic structure
- Has part
- abelian group
Show 5 more facts
- maintained by WikiProject
- WikiProject Mathematics
- different from
- absolute value
- on focus list of Wikimedia project
- Wikipedia:Vital articles/Level/4
- underlying structure
- abelian group
- studied by
- module theory
via Wikidata · CC0
~16 min read
Encyclopedic overview
In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a (not necessarily commutative) ring. The concept of a module also generalizes the notion of an abelian group, since the abelian groups are exactly the modules over the ring of integers.
Like a vector space, a module is an additive abelian group, and scalar multiplication is distributive over the operations of addition between elements of the ring or module and is compatible with the ring multiplication.
Excerpted from Wikipedia’s “module” article, available under the CC BY-SA 4.0 licence.