Discriminant of an algebraic number field

A fundamental domain of the ring of integers of the field K obtained from Q by adjoining a root of x3 − x2 − 2x + 1. This fundamental domain sits inside K ⊗QR. The discriminant of K is 49 = 72. Accordingly, the volume of the fundamental domain is 7 and K is only ramified at 7.

Richard Dedekind showed that every number field possesses an integral basis, allowing him to define the discriminant of an arbitrary number field.[15]

In mathematics, the discriminant of an algebraic number field is a numerical invariant that, loosely speaking, measures the size of the (ring of integers of the) algebraic number field. More specifically, it is proportional to the volume of the fundamental domain of the ring of integers, and it regulates which primes are ramified.

单词	Relative discriminant
释义	Relative discriminant 英语百科 Discriminant of an algebraic number field In mathematics, the discriminant of an algebraic number field is a numerical invariant that, loosely speaking, measures the size of the (ring of integers of the) algebraic number field. More specifically, it is proportional to the volume of the fundamental domain of the ring of integers, and it regulates which primes are ramified.
随便看	outfire outfish outfished outfishes outfishing outfit out fit outfit allowance Outfit Car out fit drilling out fit for outfit for hospital use,specific bloodgravity test outfit for syphilis,agglutinating method test outfit for syphilis,slide flocculation test outfiting outfit insurance outfit of deck and accommodation outfit of equipment outfits outfitter outfitting outfitting afloat outfitting basin outfitting condition outfitting dock

Relative discriminant

Discriminant of an algebraic number field