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Monomial conjecture

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 x<sub>1</sub>,&nbsp;...,&nbsp;x<sub>d</sub> be a system of parameters for A (so that A/(x<sub>1</sub>,&nbsp;...,&nbsp;x<sub>d</sub>) is an Artinian ring). Then for all positive integers&nbsp;t, we have

The statement can be relatively easily shown in characteristic zero.

See also

References