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Length of a module - Examples | | Length of a module - Examples: Encyclopedia II - Length of a module - Examples | | The zero module is the only one with length 0. Modules with length 1 are precisely the simple modules.
For every finite-dimensional vector space (viewed as a module over the base field), the length and the dimension coincide.
The length of the cyclic group Z/nZ (viewed as a module over the integers Z) is equal to the number of prime factors of n, with ...
See also:Length of a module, Length of a module - Definition, Length of a module - Examples, Length of a module - Facts | | | Length of a module, Length of a module - Definition, Length of a module - Examples, Length of a module - Facts | | |
| | | Length of a module: Encyclopedia II - Length of a module - Examples
Length of a module - Examples
The zero module is the only one with length 0. Modules with length 1 are precisely the simple modules.
For every finite-dimensional vector space (viewed as a module over the base field), the length and the dimension coincide.
The length of the cyclic group Z/nZ (viewed as a module over the integers Z) is equal to the number of prime factors of n, with multiple prime factors counted multiple times.
Other related archivesArtinian, Module theory, Noetherian, abstract algebra, composition series, cyclic group, depth, dimension, direct sum, field, height, integers, module, prime, ring, short exact sequence, simple modules, submodules, vector spaces
 Adapted from the Wikipedia article "Examples", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
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