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About: Monomial conjecture     Goto   Sponge   NotDistinct   Permalink

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Type: yago:WikicatConjecturesyago:Abstraction100002137yago:Cognition100023271yago:Concept105835747yago:Content105809192yago:Hypothesis105888929yago:Idea105833840yago:PsychologicalFeature100023100yago:Speculation105891783 New Facet based on Instances of this Class

In commutative algebra, a field of mathematics, the monomial conjecture of Melvin Hochster says the following: Let A be a Noetherian local ring of Krull dimension d and let x1, ..., xd be a system of parameters for A (so that A/(x1, ..., xd) is an Artinian ring). Then for all positive integers t, we have The statement can relatively easily be shown in characteristic zero.