In abstract algebra and number theory, Kummer theory provides a description of certain types of field extensions involving the adjunction of nth roots...

Kummer – asteroid named after Ernst Kummer Kummer configuration Kummer's congruence Kummer series Kummer theory Kummer's theorem, on prime-power divisors...

mathematics, Artin–Schreier theory is a branch of Galois theory, specifically a positive characteristic analogue of Kummer theory, for Galois extensions of...

to 1 in many programming languages. In lambda calculus and computability theory, natural numbers are represented by Church encoding as functions, where...

geometry. Algebraic number theory is also used in the study of arithmetic hyperbolic 3-manifolds. Class field theory Kummer theory Locally compact field Tamagawa...

extensions of fields (or to one of its generalizations) that leads to Kummer theory. In its most basic form, it states that if L/K is an extension of fields...

In mathematics, the Kummer–Vandiver conjecture, or Vandiver conjecture, states that a prime p does not divide the class number hK of the maximal real subfield...

profinite groups. Kummer theory The Galois theory of taking nth roots, given enough roots of unity. It includes the general theory of quadratic extensions...

elements. Also in set theory, 0 is the lowest ordinal number, corresponding to the empty set viewed as a well-ordered set. In order theory (and especially its...

In algebraic number theory, the Dedekind–Kummer theorem describes how a prime ideal in a Dedekind domain factors over the domain's integral closure. It...

solvable extensions correspond to solvable groups. Theories such as Kummer theory and class field theory are predicated on the fundamental theorem. Given...

complex numbers. These sums were known and used before Kummer, in the theory of cyclotomy. A Kummer sum is therefore a finite sum ∑ χ ( r ) e ( r / p ) =...

Thomas John Kummer (October 10, 1933 – August 9, 1969), known professionally as Jay Sebring, was an American celebrity hair stylist, and the founder of...

Eduard Kummer studied cyclic extensions of fields as part of his work on Fermat's Last Theorem. This led to the subject known as Kummer theory. Let k...

theory of abelian varieties in characteristic p (theory of Pierre Cartier). The Galois cohomology of this group scheme is a way of expressing Kummer theory...

corresponding function field extension) is cyclic. The fundamental theorem of Kummer theory implies [citation needed] that a superelliptic curve of degree m {\displaystyle...

unity, giving a non-abelian Galois group as semi-direct product. The Kummer theory gives a complete description of the abelian extension case, and the...

unity w ( P , Q ) ∈ μ n {\displaystyle w(P,Q)\in \mu _{n}} by means of Kummer theory, for any two points P , Q ∈ E ( K ) [ n ] {\displaystyle P,Q\in E(K)[n]}...

Applications Galois theory Galois group Inverse Galois problem Kummer theory General Module (mathematics) Bimodule Annihilator (ring theory) Structure Submodule...

the work of man"). Kronecker was a student and life-long friend of Ernst Kummer. Leopold Kronecker was born on 7 December 1823 in Liegnitz, Prussia (now...

application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around Diophantine geometry, the study...

integers.) The initial impetus for the development of ideal numbers (by Kummer) seems to have come from the study of higher reciprocity laws, that is,...

reducibilities and other related notions. One of the major results was Kummer's Cardinality Theory which states that a set A is computable if and only if there...

abelian varieties now includes Diophantine geometry along with class field theory, complex multiplication, local zeta-functions and L-functions. Paul Vojta...

acts as the symmetry group of the geometry. Knot theory part of topology dealing with knots Kummer theory provides a description of certain types of field...

Anabelian geometry is a theory in number theory which describes the way in which the algebraic fundamental group G of a certain arithmetic variety X,...

A Grand Unified Theory (GUT) is any model in particle physics that merges the electromagnetic, weak, and strong forces (the three gauge interactions of...

rings gives rise to class groups and regular primes, which feature in Kummer's treatment of Fermat's Last Theorem. Analysis on Lie groups and certain...

90, an important result on cyclic extensions of fields that leads to Kummer theory Hilbert's basis theorem, in commutative algebra, stating every ideal...

In algebraic geometry, a Kummer quartic surface, first studied by Ernst Kummer (1864), is an irreducible nodal surface of degree 4 in P 3 {\displaystyle...