This is a list of things named after Richard Dedekind.
Richard Dedekind
Julius Wilhelm Richard Dedekind (6 October 1831 – 12 February 1916) was a German mathematician who made important contributions to number theory, abstract algebra (particularly ring theory), and
the axiomatic foundations of arithmetic. His ...
(1831–1916), a mathematician, is the eponym of all of the things (and topics) listed below.
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19293 Dedekind
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Cantor–Dedekind axiom In mathematical logic, the Cantor–Dedekind axiom is the thesis that the Real number#Axiomatic approach, real numbers are order-isomorphic to the linear continuum of geometry. In other words, the axiom states that there is a one-to-one corresponden ...
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Dedekind completeness
In mathematics, the least-upper-bound property (sometimes called completeness or supremum property or l.u.b. property) is a fundamental property of the real numbers. More generally, a partially ordered set has the least-upper-bound property if eve ...
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Dedekind cut
In mathematics, Dedekind cuts, named after German mathematician Richard Dedekind but previously considered by Joseph Bertrand, are а method of construction of the real numbers from the rational numbers. A Dedekind cut is a partition of the rat ...
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Dedekind discriminant theorem
Julius Wilhelm Richard Dedekind (6 October 1831 – 12 February 1916) was a German mathematician who made important contributions to number theory, abstract algebra (particularly ring theory), and
the axiomatic foundations of arithmetic. His ...
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Dedekind domain
In abstract algebra, a Dedekind domain or Dedekind ring, named after Richard Dedekind, is an integral domain in which every nonzero proper ideal factors into a product of prime ideals. It can be shown that such a factorization is then necessarily ...
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Dedekind eta function
In mathematics, the Dedekind eta function, named after Richard Dedekind, is a modular form of weight 1/2 and is a function defined on the upper half-plane of complex numbers, where the imaginary part is positive. It also occurs in bosonic string t ...
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Dedekind function
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Dedekind group In group theory, a Dedekind group is a group ''G'' such that every subgroup of ''G'' is normal.
All abelian groups are Dedekind groups.
A non-abelian Dedekind group is called a Hamiltonian group.
The most familiar (and smallest) example of a Hamilt ...
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Dedekind number
File:Monotone Boolean functions 0,1,2,3.svg, 400px, The free distributive lattices of monotonic Boolean functions on 0, 1, 2, and 3 arguments, with 2, 3, 6, and 20 elements respectively (move mouse over right diagram to see description)
circle 6 ...
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Dedekind's problem
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Dedekind–Peano axioms
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Dedekind psi function
In number theory, the Dedekind psi function is the multiplicative function on the positive integers defined by
: \psi(n) = n \prod_\left(1+\frac\right),
where the product is taken over all primes p dividing n. (By convention, \psi(1), which is t ...
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Dedekind ring
In abstract algebra, a Dedekind domain or Dedekind ring, named after Richard Dedekind, is an integral domain in which every nonzero proper ideal factors into a product of prime ideals. It can be shown that such a factorization is then necessari ...
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Dedekind sum In mathematics, Dedekind sums are certain sums of products of a sawtooth function, and are given by a function ''D'' of three integer variables. Dedekind introduced them to express the functional equation of the Dedekind eta function. They have sub ...
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Dedekind valuation In algebra (in particular in algebraic geometry or algebraic number theory), a valuation is a function on a field that provides a measure of size or multiplicity of elements of the field. It generalizes to commutative algebra the notion of size in ...
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Dedekind zeta function
In mathematics, the Dedekind zeta function of an algebraic number field ''K'', generally denoted ζ''K''(''s''), is a generalization of the Riemann zeta function (which is obtained in the case where ''K'' is the field of rational numbers Q). It ca ...
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Dedekind–Hasse norm In mathematics, in particular the study of abstract algebra, a Dedekind–Hasse norm is a function on an integral domain that generalises the notion of a Euclidean function on Euclidean domains.
Definition
Let ''R'' be an integral domain and ''g' ...
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Dedekind-infinite set
In mathematics, a set ''A'' is Dedekind-infinite (named after the German mathematician Richard Dedekind) if some proper subset ''B'' of ''A'' is equinumerous to ''A''. Explicitly, this means that there exists a bijective function from ''A'' ont ...
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Dedekind–MacNeille completion
In mathematics, specifically order theory, the Dedekind–MacNeille completion of a partially ordered set is the smallest complete lattice that contains it. It is named after Holbrook Mann MacNeille whose 1937 paper first defined and constructed ...
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Dedekind's axiom
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Dedekind's complementary module In algebraic number theory, the different ideal (sometimes simply the different) is defined to measure the (possible) lack of duality in the ring of integers of an algebraic number field ''K'', with respect to the field trace. It then encodes the ...
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Dedekind lattice
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Jordan–Dedekind lattice
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bou ...
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Dedekind's theorem on ellipsoids of equilibrium
{{DEFAULTSORT:List of things named after Richard Dedekind
Dedekind, Richard