Why do we use this definition of "algebraic integer"?
A number is an "algebraic integer" if it is the root to a monic polynomial with integer coefficients. Artin says (Algebra, p. 411): The concept of algebraic integer was one of the most important …
How to prove an algebraic integer. - Mathematics Stack Exchange
Just to be clear, an algebraic integer is a root of a monic polynomial with integer coefficients. First show that the given numbers are algebraic, by finding polynomials of which they are roots (this …
Turning An Algebraic Number Into An Algebraic Integer
Jun 15, 2020 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …
Norm and Algebraic Integers - Mathematics Stack Exchange
Apr 22, 2019 · Each conjugate of an algebraic integer is an algebraic integer, because they satisfy the same polynomial.
Definition of algebraic integer - Mathematics Stack Exchange
Jul 17, 2015 · An algebraic integer is a complex number which is the root of a monic polynomial with integer coefficients. $\endgroup$ – lokodiz Commented Jul 17, 2015 at 10:34
abstract algebra - Set of algebraic integer form a ring.
An algebraic integer is a complex number that is the root of monic polynomial with integer coefficients ...
definition - Algebraic integer - Mathematics Stack Exchange
Jan 21, 2018 · A definition of algebraic number is: a complex number which is a root of a non-null polynomial with integer coefficients. The simplest and most direct way of showing that these …
abstract algebra - About algebraic integer and algebraic number ...
For eg. suppose $\beta$ is an algebraic integer satisfying $\beta^3+\beta +1$ and $\gamma$ is an algebraic integer satisfying $\gamma^2 +\gamma -3$ then it would be really hard to show …
How to prove that the sum and product of two algebraic numbers …
Addition of two algebraic integer numbers. 1. Algebraic numbers theory. 0. Sum & Product of Two Algebraic ...
abstract algebra - algebraic integers of $\mathbb{Q}(\sqrt{d ...
Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their …