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Length of a module

In algebra, the length of a module over a ring R {\displaystyle R} is a generalization of the dimension of a vector space which measures its size. page 153 It is defined to be the length of the longest chain of submodules. For vector spaces (modules over a field), the length equals the dimension. If R {\displaystyle R} is an algebra over a field k…

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Length of a module

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length displaystyle ring module finite dimension modules multiplicity chain order algebraic intersection space algebra vanishing artinian theory mathbb frac defined

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