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In mathematics and physics, the term generator or generating set may refer to any of a number of related concepts. The underlying concept in each case is that of a smaller set of objects, together with a set of operations that can be applied to it, that result in the creation of a larger collection of objects, called the generated set. The larger set is then said to be generated by the smaller set. It is commonly the case that the generating set has a simpler set of properties than the generated set, thus making it easier to discuss and examine. It is usually the case that properties of the generating set are in some way preserved by the act of generation; likewise, the properties of the generated set are often reflected in the generating set. ==List of generators== A list of examples of generating sets follow. * Generating set of a group: A set of group elements which are not contained in any subgroup of the group other than the entire group itself. * Generating set of a ring: A subset ''S'' of a ring ''A'' generates ''A'' if the only subring of ''A'' containing ''S'' is ''A'' itself. * Generating set of an ideal in a ring. * Generating set of a module; see also minimal generating set. * A generator, in category theory, is an object that can be used to distinguish morphisms. * In topology, a collection of sets which generate the topology is called a subbase. * Generating set of a topological algebra: ''S'' is a generating set of a topological algebra ''A'' if the smallest closed subalgebra of ''A'' containing ''S'' is ''A'' itself. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Generator (mathematics)」の詳細全文を読む スポンサード リンク
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