In this case the sequence is called a composition series for M. In order to prove a statement inductively using composition series, the statement is first proved for simple modules, which form the base case of the induction, and then the statement is proved to remain true under an extension of a module by a simple module.

To accomplish this extension, a tightly controlled vocabulary ( in the RSS world, " module "; in the XML world, " schema ") is declared through an XML namespace to give names to concepts and relationships between those concepts.

Most current Unix-like systems, and Microsoft Windows, support loadable kernel modules, although they might use a different name for them, such as kernel loadable module ( kld ) in FreeBSD and kernel extension ( kext ) in OS X.

* Expansion slots: SD-Card ( MultiMediaCard ) and CompactFlash Type I and II as well as PC card via an extension module

The solutions to these systems allow the extension of certain kinds of module homomorphisms.

In mathematics, a Galois module is a G-module where G is the Galois group of some extension of fields.

Given a finite separable field extension L / K and a torus T over L, we have a Galois module isomorphism

*. mpl-a file extension used to indicate an Embperl module.

* a shared library that an extant interpreter can link to as some form of extension module, or

However, as its name implies, the cable formed a loop: the cable originated in the HP-IL extension module, ran through all connected devices, then came back to the module.

* HP 82160A HP-IL HP-41 extension module ( for the HP-41C )

Among others, the standard function set offered no integration or root-finding capabilities and lacked support of matrices and complex numbers, which could be added by an extension module.

In mathematics, especially in the area of abstract algebra known as module theory, the injective hull ( or injective envelope ) of a module is both the smallest injective module containing it and the largest essential extension of it.

A module E is called the injective hull of a module M, if E is an essential extension of M, and E is injective.

* The injective hull E ( M ) is a maximal essential extension of M in the sense that if M ⊆ E ( M ) ⊊ B for a module B, then M is not an essential submodule of B.

* the discrete Heisenberg group module p is a central extension of the free abelian p-group ( Z / pZ )< sup > 2n </ sup > by a copy of Z / pZ.

The EX module code stands for extension, as the adventure is designed to be inserted as an independent addition to another, ongoing scenario.

# REDIRECT HP-41 extension module

* The extension for Fortran module files.

The AY8910 for the domestic models was sold separately as an external extension module, hanging off the same extension bus as the optional external disk drive.

On Monday, 8 May 1972, ground service equipment being used to empty the residual toxic reaction control system fuel in the command module tanks exploded in a Naval Air Station hangar.

The Expansion module is designed as a pass-through device that sits on top of the console and requires no system modding.

Some languages also include a separate, explicit namespace or module system that performs encapsulation in a more general way.

In Dylan these sorts of visibility rules are not considered part of the code itself, but of the module / interface system.

Kernel space can be accessed by user module only through the use of system calls.

An Ethertype field in each frame is used by the operating system on the receiving station to select the appropriate protocol module ( i. e. the Internet protocol module ).

In the construction and maintenance of the system there are two other roles: the problem domain expert who builds the system and supplies the knowledge base, and a knowledge engineer who assists the experts in determining the representation of their knowledge, enters this knowledge into an explanation module and who defines the inference technique required to solve the problem.

Unfortunately, the amount of speech that could be compressed into a 4K or 8K ROM cartridge was limited, and the system did not sell as well as Mattel had hoped ; while the initial orders were as high as 300, 000 units for the Intellivoice module and its initial game-cartridge offerings, interest in future titles dropped rapidly until the fourth and last Intellivoice title, Tron: Solar Sailer, sold a mere 90, 000 units.

In linear algebra, a basis is a set of linearly independent vectors that, in a linear combination, can represent every vector in a given vector space or free module, or, more simply put, which define a " coordinate system " ( as long as the basis is given a definite order ).

Mercury's module system enables division into self-contained units, a problem for past logic programming languages.

Mesa was a strongly typed programming language with type-checking across module boundaries, but with enough flexibility in its type system that heap allocators could be written in Mesa.

The main innovation of Modula over Pascal is a module system, used for grouping sets of related declarations into program units ; hence the name Modula.

Dynamically loadable modules incur a small overhead when compared to building the module into the operating system image.

The OSGi framework is a module system and service platform for the Java programming language that implements a complete and dynamic component model, something that does not exist in standalone Java / VM environments.

Siemens Simatic S7-400 system at rack, left-to-right: power supply unit PS407 4A, CPU 416-3, interface module IM 460-0 and communication processor CP 443-1.

A register transfer language is a system for expressing in symbolic form the microoperation sequences among the registers of a digital module.

R6RS features a standard module system, allowing a split between the core language and libraries.

A new module system has been introduced, and systems for exception handling are now standardized.

* Pioneer LaserActive Sega Mega-CD module, an add-on device available for the LaserActive system

This was originally intended to be Shaylle: Soldier City for the Land Beyond the Mountains campaign, but when Metagaming went out of business the module was rewritten and issued under the new title, for use with the Thieves ' Guild rules system.

This was originally intended to be Intrigue in Plaize for the Land Beyond the Mountains campaign, but when Metagaming went out of business the module was rewritten and issued under the new title, for use with the Thieves ' Guild rules system.

Slated to be an adventure module for use with the Dragons of Underearth system.

While many game companies went from FM synthesis or General MIDI in the early 1990s to CD audio and pre-rendered audio, many of the Epic games used the less common system of module music, composed with a tracker, which used stored PCM sound effects sequenced together to produce music.