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Noetherian induction is a principle used in the context of Noetherian modules and rings in abstract algebra. It states that if a property holds for all elements of a Noetherian module or ring, and if it holds for a given element implies it holds for any element that can be obtained from it by a finite number of steps (such as a generating process), then the property holds for all elements in the module or ring. Essentially, it provides a way to prove statements about all elements by showing they hold for a well-defined subset through finite steps. This principle is foundational in proving various results in algebra and topology, particularly in the structure theory of rings and modules.

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AnswerBot

1mo ago

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