Module/Related Articles: Difference between revisions
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imported>Barry R. Smith (New page: {{subpages}} ==Parent topics== {{r|abstract algebra}} ==Subtopics== ===Classes of modules defined by structural properties=== {{r|free module}} {{r|locally free module}} {{r|stably free...) |
imported>Barry R. Smith |
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{{r|locally free module}} | {{r|locally free module}} | ||
{{r|stably free module}} | {{r|stably free module}} | ||
{{r|projective module}} | |||
{{r|injective module}} | |||
{{r|Noetherian module}} | {{r|Noetherian module}} | ||
{{r|Artinian module}} | {{r|Artinian module}} | ||
Revision as of 11:30, 29 November 2008
- See also changes related to Module, or pages that link to Module or to this page or whose text contains "Module".
Parent topics
- Abstract algebra [r]: Branch of mathematics that studies structures such as groups, rings, and fields. [e]
Subtopics
Classes of modules defined by structural properties
- Free module [r]: Add brief definition or description
- Locally free module [r]: Add brief definition or description
- Stably free module [r]: A module which is close to being free: the direct sum with some free module is free. [e]
- Projective module [r]: Add brief definition or description
- Injective module [r]: Add brief definition or description
- Noetherian module [r]: Module in which every ascending sequence of submodules has only a finite number of distinct members. [e]
- Artinian module [r]: Add brief definition or description
- Finitely-generated module [r]: Add brief definition or description
- Semi-simple module [r]: Add brief definition or description
- Simple module [r]: Add brief definition or description
Modules over special types of rings
- Abelian group [r]: A group in which the group operation is commutative. [e]
- Vector space [r]: A set of vectors that can be added together or scalar multiplied to form new vectors [e]
- Galois module [r]: Add brief definition or description
- Principal ideal domain [r]: Add brief definition or description
- Dedekind domain [r]: A Noetherian domain, integrally closed in its field of fractions, of which every prime ideal is maximal. [e]
- Iwasawa module [r]: Add brief definition or description
Modules occurring in practice
- Homology groups [r]: Add brief definition or description
- Class groups [r]: Add brief definition or description