Jump to content

Monomial conjecture

From Wikipedia, the free encyclopedia

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

The statement can relatively easily be shown in characteristic zero.

See also

[edit]

References

[edit]
  1. ^ "Local Cohomology and the Homological Conjectures in Commutative Algebra" (PDF). www5a.biglobe.ne.jp. Retrieved 2023-12-19.