A Module

1. A self-contained component of a system, often interchangeable, which has a well-defined interface to the other components.
2. (architecture) A standard unit of measure used for determining the proportions of a building.
3. (programming) A section of a program; a subroutine or group of subroutines.
4. A unit of education covering a single topic.
5. A pre-prepared adventure scenario with related materials for a role-playing game.
6. (algebra, ring theory) An abelian group equipped with the operation of multiplication by an element of a ring (or another of certain algebraic objects), representing a generalisation of the concept of vector space with scalar multiplication. Meronym: element
7. (fractal geometry, mathematics) A fractal element.
8. (music) A file containing a music sequence that can be played in a tracker (called also mod or music module).
9. (hydraulics) A contrivance for regulating the supply of water from an irrigation channel.
10. (astronautics) An independent self-contained unit of a spacecraft.

Usage notes

• (abelian group equipped with multiplication by an element of a ring):
  • For a given ring R, one speaks of an "R-module" or, equivalently, of a "module over R". R is expected to be unital.
  • R may also be a Lie algebra.
  • If K is a field, "K-module" is identical to "K-vector space".
  • If the ring is not commutative, scalar multiplication of a module is defined as left- and/or right-multiplication, and one refers to a "left R-module" or a "right R-module".
  • The concept of module is closely connected to the representation theory of groups and is central to both commutative algebra and homological algebra. Modules are also widely used in algebraic geometry and algebraic topology.