“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.
随便看	ribbon diagram ribbon jasper ribbon lakes ribbon microphone ribbons ribbon worm riboflavin ribonuclease ribonucleic acid ribonucleoprotein ribose ribosomal RNA ribosome riboswitch ribotyping ribozyme ribulose ribulose bisphosphate Ricardian equivalence Ricardo, David (1772–1823) Ricci, Matteo (1552–1610) Riccioli, Giovanni Battista Rice, Condoleezza (1954) Rice–Herzfeld mechanism Rice–Ramsperger–Kassel theory