In algebra (in particular in algebraic geometry or algebraic number theory), a valuation is a function on a field that provides a measure of the size...
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Valuation: Measuring and Managing the Value of Companies Valuation (algebra), a measure of multiplicity p-adic valuation, a special case Valuation (geometry)...
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In abstract algebra, a discrete valuation ring (DVR) is a principal ideal domain (PID) with exactly one non-zero maximal ideal. This means a DVR is an...
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{\displaystyle \mathbb {Q} _{p}} of p-adic numbers. p-adic number Valuation (algebra) Archimedean property Multiplicity (mathematics) Ostrowski's theorem...
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Hilbert polynomial Regular local ring Discrete valuation ring Global dimension Regular sequence (algebra) Krull dimension Krull's principal ideal theorem...
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In abstract algebra, a valuation ring is an integral domain D such that for every non-zero element x of its field of fractions F, at least one of x or...
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= R {\displaystyle \pi _{x}(R)=R} . Valuation algebras Dropping the idempotency axiom leads to valuation algebras. These axioms have been introduced by...
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shortest path problem. Action algebra Algebraic structure Kleene star Regular expression Star semiring Valuation algebra Marc Pouly; Jürg Kohlas (2011)...
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Unicode symbols for CJK Compatibility includes SI Unit symbols Valuation (algebra), an algebraic generalization of "order of magnitude" Scale (analytical tool)...
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Euclidean domain (redirect from Euclidean valuation)
norm-Euclidean and is one of the five first fields in the preceding list. Valuation (algebra) Rogers, Kenneth (1971), "The Axioms for Euclidean Domains", American...
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manifold Weil restriction Differential Galois theory Prime ideal Valuation (algebra) Krull dimension Regular local ring Regular sequence Cohen–Macaulay...
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Tropical semiring (redirect from Min-plus algebra)
in Brazil. The min tropical semiring (or min-plus semiring or min-plus algebra) is the semiring ( R ∪ { + ∞ } {\displaystyle \mathbb {R} \cup \{+\infty...
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Field (mathematics) (redirect from Field (algebra))
and real numbers. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics...
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main class of commutative rings occurring in algebraic number theory), integral extensions, and valuation rings. Polynomial rings in several indeterminates...
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denote a valuation; that is, v ( ϕ ) = [ [ ϕ ] ] v {\displaystyle v(\phi )=[\![\phi ]\!]_{v}} for a proposition ϕ {\displaystyle \phi } . Algebraic semantics...
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Ring (mathematics) (redirect from Ring (algebra))
k^{*}\right).} Azumaya algebras generalize the notion of central simple algebras to a commutative local ring. If K is a field, a valuation v is a group homomorphism...
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In algebra, an absolute value (also called a valuation, magnitude, or norm, although "norm" usually refers to a specific kind of absolute value on a field)...
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Local ring (redirect from Local algebra)
Nathan (2009). Basic algebra. Vol. 2 (2nd ed.). Dover. ISBN 978-0-486-47187-7. Discrete valuation ring Semi-local ring Valuation ring Gorenstein local...
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Semiring (redirect from Rig (algebra))
of sets – Family closed under unions and relative complements Valuation algebra – Algebra describing information processingPages displaying short descriptions...
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Shortest path problem (redirect from Algebraic path problem)
obviously related problems) has been developed under the banner of valuation algebras. In real-life situations, the transportation network is usually stochastic...
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values, valuations, places and their completions. Given an algebraic function field K/k of one variable, we define the notion of a valuation ring of K/k:...
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In a similar manner, one also defines a discrete valuation on the function field of an algebraic curve for every regular point p {\displaystyle p} on...
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Ostrowski's theorem (category Theorems in algebraic number theory)
numbers. This is sometimes also referred to as Ostrowski's theorem. Valuation (algebra) Koblitz, Neal (1984). P-adic numbers, p-adic analysis, and zeta-functions...
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Puiseux series (category Commutative algebra)
{\displaystyle x=t^{n}+\cdots } (since K {\displaystyle K} is algebraically closed, we can assume the valuation coefficient to be 1) and y = c t k + ⋯ {\displaystyle...
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Local field (redirect from Normalized valuation)
local fields show up as the completions of algebraic number fields with respect to their discrete valuation corresponding to one of their maximal ideals...
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a local field with valuation v and D a K-algebra. We may assume D is a division algebra with centre K of degree n. The valuation v can be extended to...
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In mathematics, an algebraic number field (or simply number field) is an extension field K {\displaystyle K} of the field of rational numbers Q {\displaystyle...
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Truth value (section Algebraic semantics)
But even non-truth-valuational logics can associate values with logical formulae, as is done in algebraic semantics. The algebraic semantics of intuitionistic...
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Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations...
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Regular local ring (redirect from Regular ring (in commutative algebra))
In commutative algebra, a regular local ring is a Noetherian local ring having the property that the minimal number of generators of its maximal ideal...
12 KB (1,874 words) - 10:09, 18 February 2024