module
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generalization of vector space, with scalars in a ring instead of a field
~16 min read
Article
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.
Connections
algebra over a field
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distributive property
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modular arithmetic
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algebraic structure
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ideal
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category
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Lie algebra
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p-adic number
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free module
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graded ring
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ascending chain condition
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direct sum
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non-associative algebra
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annihilator
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near-ring
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noncommutative ring
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preadditive category
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mathematics
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International Standard Book Number
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natural number
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