Noetherian Modules
نویسنده
چکیده
In a finite-dimensional vector space, every subspace is finite-dimensional and the dimension of a subspace is at most the dimension of the whole space. Unfortunately, the naive analogue of this for modules and submodules is wrong: (1) A submodule of a finitely generated module need not be finitely generated. (2) Even if a submodule of a finitely generated module is finitely generated, the minimal number of generators of the submodule is not bounded above by the minimal number of generators of the original module.
منابع مشابه
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