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>, ..., x<sub>d</sub> be a system of parameters for A (so that A/(x<sub>1</sub>, ..., x<sub>d</sub>) is an Artinian ring). Then for all positive integers t, we have
The statement can be relatively easily shown in characteristic zero.