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15 relations: Character theory, Characteristic (algebra), Complete metric space, Dirichlet character, Discrete valuation ring, Graduate Texts in Mathematics, Hensel's lemma, Number theory, Oswald Teichmüller, P-adic number, Perfect field, Section (category theory), Springer Science+Business Media, Valuation (algebra), Witt vector.
Character theory
In mathematics, more specifically in group theory, the character of a group representation is a function on the group that associates to each group element the trace of the corresponding matrix.
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Characteristic (algebra)
In mathematics, the characteristic of a ring R, often denoted char(R), is defined to be the smallest number of times one must use the ring's multiplicative identity (1) in a sum to get the additive identity (0) if the sum does indeed eventually attain 0.
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Complete metric space
In mathematical analysis, a metric space M is called complete (or a Cauchy space) if every Cauchy sequence of points in M has a limit that is also in M or, alternatively, if every Cauchy sequence in M converges in M. Intuitively, a space is complete if there are no "points missing" from it (inside or at the boundary).
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Dirichlet character
In number theory, Dirichlet characters are certain arithmetic functions which arise from completely multiplicative characters on the units of \mathbb Z / k \mathbb Z. Dirichlet characters are used to define Dirichlet ''L''-functions, which are meromorphic functions with a variety of interesting analytic properties.
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Discrete valuation ring
In abstract algebra, a discrete valuation ring (DVR) is a principal ideal domain (PID) with exactly one non-zero maximal ideal.
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Graduate Texts in Mathematics
Graduate Texts in Mathematics (GTM) (ISSN 0072-5285) is a series of graduate-level textbooks in mathematics published by Springer-Verlag.
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Hensel's lemma
In mathematics, Hensel's lemma, also known as Hensel's lifting lemma, named after Kurt Hensel, is a result in modular arithmetic, stating that if a polynomial equation has a simple root modulo a prime number, then this root corresponds to a unique root of the same equation modulo any higher power of, which can be found by iteratively "lifting" the solution modulo successive powers of.
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Number theory
Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.
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Oswald Teichmüller
Paul Julius Oswald Teichmüller (18 June 1913 – 11 September 1943) was a German mathematician who introduced quasiconformal mappings and differential geometric methods into the study of Riemann surfaces.
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P-adic number
In mathematics, the -adic number system for any prime number extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems.
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Perfect field
In algebra, a field k is said to be perfect if any one of the following equivalent conditions holds.
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Section (category theory)
In category theory, a branch of mathematics, a section is a right inverse of some morphism.
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Springer Science+Business Media
Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
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Valuation (algebra)
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.
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Witt vector
In mathematics, a Witt vector is an infinite sequence of elements of a commutative ring.
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