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    Modul

    Alternate name
    Basic definition

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

    Detailed definition

    A module is a mathematical object in which things can be added together commutatively by multiplying coefficients and in which most of the rules of manipulating vectors hold. A module is abstractly very similar to a vector space, although in modules, coefficients are taken in rings that are much more general algebraic objects than the fields used in vector spaces. A module taking its coefficients in a ring R is called a module over R, or a R-module.
Modules are the basic tool of homological algebra. Examples of modules include the set of integers Z, the cubic lattice in d dimensions Z^d, and the group ring of a group.

    Educational grade level

    graduate school level

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