Dimension Inequality
Serre proved this for all regular local rings. He established the following three properties when R is either of equal characteristic or of mixed characteristic and unramified (which in this case means that characteristic of the residue field is not an element of the square of the maximal ideal of the local ring), and conjectured that they hold in general.
Read more about this topic: Serre's Multiplicity Conjectures
Famous quotes containing the words dimension and/or inequality:
“Le Corbusier was the sort of relentlessly rational intellectual that only France loves wholeheartedly, the logician who flies higher and higher in ever-decreasing circles until, with one last, utterly inevitable induction, he disappears up his own fundamental aperture and emerges in the fourth dimension as a needle-thin umber bird.”
—Tom Wolfe (b. 1931)
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—Henry David Thoreau (1817–1862)