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Module

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A module is a generalization of a vector space in which the scalars form a ring rather than a field.

Module is a graduate-level concept that would be first encountered in an abstract algebra course covering rings and fields.

Examples

Integer: An integer is one of the numbers ..., -2, -1, 0, 1, 2, ....

Prerequisites

Field: A field is a ring in which every nonzero element has a multiplicative inverse. The real numbers and the complex numbers are both fields.
Ring: In mathematics, a ring is an Abelian group together with a rule for multiplying its elements.
Vector Space: A vector space is a set that is closed under finite vector addition and scalar multiplication. The basic example is n-dimensional Euclidean space.

Classroom Articles on Rings and Fields

  • Algebra
  • Gaussian Integer
  • Algebraic Number
  • Ideal
  • Finite Field
  • Quaternion

  • Classroom Articles on Abstract Algebra (Up to Graduate Level)

  • Abelian Group
  • Group Representation
  • Abstract Algebra
  • Group Theory
  • Algebraic Variety
  • Isomorphism
  • Boolean Algebra
  • Lie Algebra
  • Category
  • Lie Group
  • Cyclic Group
  • Normal Subgroup
  • Dihedral Group
  • Simple Group
  • Finite Group
  • Subgroup
  • Group
  • Symmetric Group
  • Group Action
  • Symmetry Group