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{{short description|Study of algorithms for performing number theoretic computations}} | title = Algorithmic Number Theory, Volume 1: Efficient Algorithms

{{Short description|Complex number with rational components}} ...ewart (mathematician)|Ian Stewart]], [[David O. Tall]], ''Algebraic Number Theory'', [[Chapman and Hall]], 1979, {{ISBN|0-412-13840-9}}. Chap.3.</ref>

{{Short description|Complex number that is a root of a non-zero polynomial in one variable with rational coeff ...ंख्याएं नहीं हैं (लिंडमैन-वीयरस्ट्रास प्रमेय देखें)।<ref>Also, [[Liouville number|Liouville's theorem]] can be used to "produce as many examples of transcend

...em" redirects here. For the branch of Galois theory, see [[Artin–Schreier theory]].}} ...ers, the field of real [[algebraic number]]s, and the field of [[hyperreal number]]s.

...I.4}}. This is the situation in which the formalism of [[local class field theory]] works.</ref> | title=Class field theory

{{Short description|Algebraic field extension}} *{{cite book|last=Artin | first=Emil | title=Galois Theory | publisher=Dover Publications | year=1998 | orig-year=1944 | isbn=0-486-62

{{Short description|Algebraic field extension}} *{{cite book|last=Artin | first=Emil | title=Galois Theory | publisher=Dover Publications | year=1998 | orig-year=1944 | isbn=0-486-62

...]], [[97 (number)|97]], [[101 (number)|101]], [[109 (number)|109]], [[113 (number)|113]], ... {{OEIS|id=A002144}}.}} | title = Spectral Graph Theory

In [[mathematics]], '''operator theory''' is the study of [[linear operator]]s on [[function space]]s, beginning w ...erator algebra]]. The description of operator algebras is part of operator theory.

...ort description|Mathematical group occurring in algebraic geometry and the theory of complex manifolds}} ...ki, t. 14: année 1961/62, exposés 223-240, no. 7, Talk no. 232 |year=1962 |number=7|pages=143–161}}

...95}}</ref><ref>{{springer|id=M/m110160|first=S.|last= Kuhlmann|title=Model theory of the real exponential function}}</ref> इसके विपरीत, [ ...ओं का कुशल समाधान|journal=ACM Transactions on Computational Logic|volume=7|number=4|year=2006}}</ref> वैकल्पिक रूप से, विशु

...class of "simple" [[function (mathematics)|functions]] which preserve the algebraic structure of [[linear space]]s and are often used as approximations to more ...ed, and so is actually a [[linear functional]] on ''X'' (an element of the algebraic [[dual space]] ''X''^*). The linear map ''X'' → ''X'' which as

Given a vector space <math>X</math> over the [[real number]]s <math>\Reals</math> and a [[preorder]] <math>\,\leq\,</math> on the [[se ...ng <math>x \mapsto -x</math> is an [[isomorphism]] to the [[Duality (order theory)|dual order structure]]. Ordered vector spaces are [[ordered group]]s under

...a]] |isbn=978-3-540-93806-4 |chapter=An Introduction to Ring-Linear Coding Theory |author-first=Marcus |author-last=Greferath |page=[https://archive.org/deta ...कों पर कोड|journal=[[IEEE Transactions on Information Theory]] |volume=40 |number=1 |pages=207–216 |date=January<!-- February --> 1994 |orig-date=1993-01-1

...2-last= Fröhlich | editor2-link=Albrecht Fröhlich | title=Algebraic Number Theory | year=1967 | zbl=0153.07403}}

{{Ring theory sidebar|Basic}} ...used to construct a [[quotient ring]] in a way similar to how, in [[group theory]], a [[normal subgroup]] can be used to construct a [[quotient group]].

...ो सकते हैं जबकि एक प्रमुख आदर्श प्रांत नहीं हो सकता है।{{short description|Algebraic structure}} {{Algebraic structures |Ring}}

...[[order theory]]). This article focuses on prime ideal theorems from order theory. ...FC) that the Boolean prime ideal theorem is often taken as an axiom of set theory. The abbreviations BPI or PIT (for Boolean algebras) are sometimes used to

* Any set of [[cardinal number]]s or [[ordinal number]]s (more strongly, these are [[well-order]]s). ...he term is used for stating properties of the set of the chains. This high number of nested levels of sets explains the usefulness of the term.

...Finding a complete list of imaginary quadratic fields having a given class number}} ...://www.claymath.org/publications/Gauss_Dirichlet/stark.pdf The Gauss Class-Number Problems], by H. M. Stark</ref>