Monomial conjecture
From HandWiki
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, ..., 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
- [math]\displaystyle{ x_1^t \cdots x_d^t \not\in (x_1^{t+1},\dots,x_d^{t+1}). \, }[/math]
The statement can relatively easily be shown in characteristic zero.
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