algebraic number field oor Sloweens

algebraic number field

naamwoord

number field

Vertalings in die woordeboek Engels - Sloweens

Obseg algebrskih števil

voorbeelde

The extended Riemann hypothesis extends the Riemann hypothesis to all Dedekind zeta functions of algebraic number fields.
Razširjena Riemannova domenva razširi Riemannovo domnevo za vse Dedekindove funkcije ζ obsegov algebrskih števil.

Weinberger (1973) showed that the generalized Riemann hypothesis for the zeta functions of all algebraic number fields implies that any number field with class number 1 is either Euclidean or an imaginary quadratic number field of discriminant −19, −43, −67, or −163.
Weinberger je leta 1973 pokazal, da iz posplošene Riemannove domneve za funkcije ζ vseh obsegov argebrskih števil izhaja, da je vsak obseg z razrednim številom 1 ali evklidski ali imaginarni kvadratni številski obseg diskriminant −19, −43, −67 ali −163.

When one goes from geometric dimension one, e.g. an algebraic number field, to geometric dimension two, e.g. a regular model of an elliptic curve over a number field, the two-dimensional part of the generalized Riemann hypothesis for the arithmetic zeta function of the model deals with the poles of the zeta function.
Če se prestopi iz geometrične razsežnosti 1, na primer obsega algebrskih števil, na geometrično razsežnost 2, na primer model eliptične krivulje čez številski obseg, dvorazsežni del posplošene Riemannove domneve za aritmetično funkcijo ζ modela obravnava pole funkcije ζ.

The Frobenius theorem states that up to isomorphism there are three such algebras: the reals themselves (dimension 1), the field of complex numbers (dimension 2), and the quaternions (dimension 4).
Frobeniusov izrek trdi, da so glede na morfizem štiri takšne algebre: realna števila (razsežnost 1), kompleksna števila (razsežnost 2), kvaternioni (razsežnost 4) ter oktonioni (razsežnost 8).

In part, the growth was spurred by new connections and applications to other fields, ranging from algebra to probability, from functional analysis to number theory, etc. These connections shed the boundaries between combinatorics and parts of mathematics and theoretical computer science, but at the same time led to a partial fragmentation of the field.
Deloma je bila rast pogojena z novimi povezavami in uporabami na drugih področjih, od algebre do verjetnosti, od funkcionalne analize do teorije števil, itd. Te povezave so prelile meje med kombinatoriko in deli matematike ter teoretičnega računalništva, istočasno pa so vodile do delne razdrobitve področja.

Thesis: “Group of units in the field of algebraic numbers”.
Diplomsko delo: “Grupa enot v obsegu algebraičnih števil”.

By its great generality, abstract algebra can often be applied to seemingly unrelated problems; for instance a number of ancient problems concerning compass and straightedge constructions were finally solved using Galois theory, which involves field theory and group theory.
Abstraktna algebra se pogosto lahko uporabi za navidezno nepovezane probleme; na primer: kar nekaj antičnih problemov, ki zadevajo geometrijsko konstrukcijo so rešili z uporabo Galoisove teorije, ki vključuje teorijo obsegov in teorijo grup.

Arithmetic with infinity does not obey all of the usual rules of algebra, and so the extended complex numbers do not form a field.
Računanje z neskončnostjo ne sledi običajnim algebrskim pravilom in zaradi tega razširjena komplesna števila ne tvorijo obseg.

"for seminal contributions to algebraic geometry and for their transformative impact on number theory, representation theory, and related fields"
»za plodonosne prispevke k algebrski geometriji in za njihov preobrazni vpliv na teorijo števil, teorijo reprezentacij in sorodna področja.«

In mathematics, real is used as an adjective, meaning that the underlying field is the field of the real numbers (or the real field). For example, real matrix, real polynomial and real Lie algebra.
V matematiki se pridevnik »realni« (npr. realna matrika, realni polinom, realna Liejeva algebra) uporablja za označitev dejstva, da je obseg, ki je podlaga tem pojmom, obseg realnih števil.