“module”的概念、定义、翻译、参考文献-科学参考

module

Mathematics

An equivalent idea to a vector space but where scalars are from a ring which need not be a field. Given a ring R with a multiplicative identity 1, an R-module M is an abelian group together with a notion of scalar multiplication (r,m) ↦r∙m, which further satisfies

$(r_{1} + r_{2}) \cdot m = r_{1} \cdot m + r_{2} \cdot m, (r_{1} r_{2}) \cdot m = r_{1} \cdot (r_{2} \cdot m), r \cdot (m_{1} + m_{2}) = r \cdot m + r \cdot m_{2}, 1 \cdot m = m,$

for all r₁,r₂,r in R and m₁,m₂,m in M. Typically R is further assumed to be a principal ideal domain or a Euclidean domain. ℤ-modules are abelian groups and vice versa. An F[x]-module, where F is a field, is a vector space V over F together with a linear map x:V → V defining scalar multiplication by x. Modules are intimately connected with representation theory. See free module, Jordan normal form, rational canonical form, Smith normal form, structure theorem, torsion element.

Space Exploration

A component of a spacecraft. Modules are designed in coordination. For the Apollo Moon landings, the craft comprised a command module (for working, eating, sleeping), service module (electricity generators, oxygen supplies, manoeuvring rocket), and lunar module (to land and return the astronauts).

Computer

1. A programming or specification construct that defines a software component. Often a module is a unit of software that provides users with some data types and operations on those data types, and can be separately compiled. The module has an interface in the form of a heading that specifies the data types and operations the module provides its users. Mathematically, the syntax of the interface is a signature and the semantics of a module is a class of algebras of that signature. In some programming languages that provide modules, they are called by other names such as package, cluster, or object. The concept developed as a programming construct to support information hiding and abstract data types. The theory of program construction based on modules is a promising, but difficult, area of research.
2. A component of a hardware system that can be subdivided.

Internet

A hardware chunk or software chunk that makes up a hardware, software, or mixed system. Modules almost invariably have well-designed interfaces which other modules can connect to. See also modular architecture.

单词	module
释义	module Mathematics An equivalent idea to a vector space but where scalars are from a ring which need not be a field. Given a ring R with a multiplicative identity 1, an R-module M is an abelian group together with a notion of scalar multiplication (r,m) ↦r∙m, which further satisfies $(r_{1} + r_{2}) \cdot m = r_{1} \cdot m + r_{2} \cdot m, (r_{1} r_{2}) \cdot m = r_{1} \cdot (r_{2} \cdot m), r \cdot (m_{1} + m_{2}) = r \cdot m + r \cdot m_{2}, 1 \cdot m = m,$ for all r₁,r₂,r in R and m₁,m₂,m in M. Typically R is further assumed to be a principal ideal domain or a Euclidean domain. ℤ-modules are abelian groups and vice versa. An F[x]-module, where F is a field, is a vector space V over F together with a linear map x:V → V defining scalar multiplication by x. Modules are intimately connected with representation theory. See free module, Jordan normal form, rational canonical form, Smith normal form, structure theorem, torsion element. Space Exploration A component of a spacecraft. Modules are designed in coordination. For the Apollo Moon landings, the craft comprised a command module (for working, eating, sleeping), service module (electricity generators, oxygen supplies, manoeuvring rocket), and lunar module (to land and return the astronauts). Computer 1. A programming or specification construct that defines a software component. Often a module is a unit of software that provides users with some data types and operations on those data types, and can be separately compiled. The module has an interface in the form of a heading that specifies the data types and operations the module provides its users. Mathematically, the syntax of the interface is a signature and the semantics of a module is a class of algebras of that signature. In some programming languages that provide modules, they are called by other names such as package, cluster, or object. The concept developed as a programming construct to support information hiding and abstract data types. The theory of program construction based on modules is a promising, but difficult, area of research. 2. A component of a hardware system that can be subdivided. Internet A hardware chunk or software chunk that makes up a hardware, software, or mixed system. Modules almost invariably have well-designed interfaces which other modules can connect to. See also modular architecture.
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