“Monomial conjecture”的意思、由来-开放百科全书

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Monomial conjecture

释义

References

In commutative algebra, a field of mathematics, the monomial conjecture of Melvin Hochster says the following:^[1]

Let A be a Noetherian local ring of Krull dimension d and let x₁, ..., x_d be a system of parameters for A (so that A/(x₁, ..., x_d) is an Artinian ring. Then for all positive integers t, we have

The statement can relatively easily be shown in characteristic zero.

References

1. ^http://www5a.biglobe.ne.jp/~tomari/hamana/roberts.pdf

2 : Commutative algebra|Conjectures

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