The monomial conjecture, in commutative algebra, is an open conjecture proposed by the mathematician Melvin Hochster.
Facts
StatementFor a Noetherian local ring A of Krull dimension d with a system of parameters x_1 through x_d, for every positive integer t the product of the x_i each raised to the power t is not in the ideal generated by the x_i each raised to the power t plus 1. 1 Progress Toward ResolutionThe monomial conjecture can be relatively easily shown to hold in characteristic zero. 1 Classification
Resolution Status Prize Status
Prize Status (category) Connections
In Branch
Source Monomial Conjecture, Wikipedia
Sources
1. Monomial Conjecture, Wikipedia
Lead section
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 x1, ..., xd be a system of parameters for A (so that A/(x1, ..., xd) is an Artinian ring).
Introduction section, second paragraph
The statement can be relatively easily shown in characteristic zero.
- Lead section
In Branch: Commutative Algebra, Lead sentence
In commutative algebra, a field of mathematics, the monomial conjecture of Melvin Hochster says the following: Let A be a Noetheri
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