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...

Valuation: Measuring and Managing the Value of Companies Valuation (algebra), a measure of multiplicity p-adic valuation, a special case Valuation (geometry)...

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...

{\displaystyle \mathbb {Q} _{p}} of p-adic numbers. p-adic number Valuation (algebra) Archimedean property Multiplicity (mathematics) Ostrowski's theorem...

Hilbert polynomial Regular local ring Discrete valuation ring Global dimension Regular sequence (algebra) Krull dimension Krull's principal ideal theorem...

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...

= R {\displaystyle \pi _{x}(R)=R} . Valuation algebras Dropping the idempotency axiom leads to valuation algebras. These axioms have been introduced by...

shortest path problem. Action algebra Algebraic structure Kleene star Regular expression Star semiring Valuation algebra Marc Pouly; Jürg Kohlas (2011)...

Unicode symbols for CJK Compatibility includes SI Unit symbols Valuation (algebra), an algebraic generalization of "order of magnitude" Scale (analytical tool)...

manifold Weil restriction Differential Galois theory Prime ideal Valuation (algebra) Krull dimension Regular local ring Regular sequence Cohen–Macaulay...

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...

in Brazil. The min tropical semiring (or min-plus semiring or min-plus algebra) is the semiring ( R ∪ { + ∞ } {\displaystyle \mathbb {R} \cup \{+\infty...

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...

main class of commutative rings occurring in algebraic number theory), integral extensions, and valuation rings. Polynomial rings in several indeterminates...

denote a valuation; that is, v ( ϕ ) = [ [ ϕ ] ] v {\displaystyle v(\phi )=[\![\phi ]\!]_{v}} for a proposition ϕ {\displaystyle \phi } . Algebraic semantics...

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...

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)...

of sets – Family closed under unions and relative complements Valuation algebra – Algebra describing information processingPages displaying short descriptions...

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...

obviously related problems) has been developed under the banner of valuation algebras. In real-life situations, the transportation network is usually stochastic...

{\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...

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...

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:...

local fields show up as the completions of algebraic number fields with respect to their discrete valuation corresponding to one of their maximal ideals...

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...

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...

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...

But even non-truth-valuational logics can associate values with logical formulae, as is done in algebraic semantics. The algebraic semantics of intuitionistic...

numbers. In algebraic number theory, the integers are sometimes qualified as rational integers to distinguish them from the more general algebraic integers...

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...