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Asynchronous module definition (AMD) is a specification for the programming language JavaScript. It defines an application programming interface (API) that defines code modules and their dependencies, and loads them asynchronously if desired. Implementations of AMD provide the following benefits:
Modular programming is a software design technique that emphasizes separating the functionality of a program into independent, interchangeable modules, such that each contains everything necessary to execute only one aspect or "concern" of the desired functionality. A module interface expresses the elements that are provided and required by the ...
Every vector space is a free module, [1] but, if the ring of the coefficients is not a division ring (not a field in the commutative case), then there exist non-free modules. Given any set S and ring R, there is a free R-module with basis S, which is called the free module on S or module of formal R-linear combinations of the elements of S.
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However, if the lead can't capture the "introduction to" aspect due to the level of understanding required to introduce the topic, and the article would benefit from a "middle level" of summary between lead and full article, one way to solve that problem is with an "Introduction to" style article.
The most basic example of a semisimple module is a module over a field, i.e., a vector space. On the other hand, the ring Z of integers is not a semisimple module over itself, since the submodule 2Z is not a direct summand. Semisimple is stronger than completely decomposable, which is a direct sum of indecomposable submodules.
Indeed, for any right module M, it is automatically a left module over the ring of integers Z, and moreover is a Z-R-bimodule. For example, consider the rational numbers Q as a Z-Q-bimodule in the natural way. Then Q is not Artinian as a left Z-module, but it is Artinian as a right Q-module.
Unfortunately, it is not ready, and I can't see it being stable within a few weeks. The number of bugs being identified is increasing fast. The number of bugs being identified is increasing fast. As a bare minimum, the parser must be approaching perfect - problems causing dirty diffs must be fixed within a few days, which means having ...