Everything about Algebraic integer
Complex number that solves a monic polynomial with integer coefficients
In algebraic number theory, an algebraic integer is a complex number that is integral over the integers. That is, an algebraic integer is a complex root of some polynomial which is monic and has coefficients that are all integers. The set of all algebraic integers A is closed under addition, subtraction and multiplication and therefore is a commutative subring of the complex numbers. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Algebraic integerA 5-minute orientation
- Skim a recent paper: Algebraic-integer valued polynomialsInfluential work since 2022
- Pick up a classic book: FactorizationThe most-reprinted book on the subject
- Read the landmark paper: On the complexity of algebraic numbers I. Expansions in integer basesCited 94 times
- Go sideways: Algebraic numberA closely related topic
- Go sideways: Algebraic number fieldA closely related topic
📖 Definitions
Noun A real or complex number (more generally, an element of a number field) which is a root of a monic polynomial whose coefficients are integers; equivalently, an algebraic number whose minimal polynomial (lowest-degree polynomial of which it is a root and whose leading coefficient is 1) has integer coefficients.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
On the complexity of algebraic numbers I. Expansions in integer bases
Diophantine sets over algebraic integer rings. II
On the Distribution of Integer Ideals in Algebraic Number Fields
Trace of totally positive algebraic integers and integer transfinite diameter
Every totally real algebraic integer is a tree eigenvalue
On prime divisors of the index of an algebraic integer
A New Algebraic Geometry Algorithm for Integer Programming
An algebraic approach to integer portfolio problems
🆕 Influential since 2022
Algebraic-integer valued polynomials
On certain polytopes associated to products of algebraic integer conjugates
Memory-efficient Very Large Scale Integration Architecture of 2D Algebraic-integer-based Daubechies Discrete Wavelet Transform
Algebraic Structures and Combinatorial Properties of Unit Graphs in Rings of Integer Modulo with Specific Orders
ALGEBRAIC DEGREE OF SERIES OF RECIPROCAL ALGEBRAIC INTEGERS
📚 Books worth reading
FactorizationSteven H. Weintraub · 2008
Algebraic geometry codesM. A. Tsfasman, Michael Tsfasman · 2007
Integer-valued polynomialsPaul-Jean Cahen · 1997- 📕A-divisible modules, period maps, and quasi-canonical liftingsJiu-Kang Yu · 1994
Iteration (The Tool Kit of Dynamic Activities)Jonathan Choate, Robert Devaney · 1999
Elliptic functions and rings of integersPh Cassou-Noguès · 1987- 📕Hopf Algebras and Galois Module TheoryLindsay Childs · 2021
Algebraic StatisticsSeth Sullivant · 2018
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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