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
| t | |
| x | |
| 1 |
…
| t | |
| x | |
| d |
\not\in
| t+1 | |
| (x | |
| 1 |
| t+1 | |
| ,...,x | |
| d |
).
The statement can relatively easily be shown in characteristic zero.