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Tag Archives: length of module
Commutative Algebra 37
Artinian Modules Instead of the ascending chain condition, we can take its reverse. Definition. Let M be an A-module. Consider the set of submodules of M, ordered by inclusion, i.e. if and only if . We say M is artinian … Continue reading
Posted in Advanced Algebra
Tagged artinian, composition factors, composition series, length of module, noetherian, simple modules
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Composition Series
Positive integers can be uniquely factored as a product of primes. Here, we would like to prove a counterpart for modules. Now there are two ways to “factor” a module M; a more liberal way takes a submodule N which gives us composition … Continue reading
Posted in Notes
Tagged algebra, artinian, composition series, length of module, matrix rings, modules, noetherian, unique factorisation
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Mathematics and Such 