TOPICS
Search

Algebraic Number Theory


Algebraic number theory is the branch of number theory that deals with algebraic numbers. Historically, algebraic number theory developed as a set of tools for solving problems in elementary number theory, namely Diophantine equations (i.e., equations whose solutions are integers or rational numbers). Using algebraic number theory, some of these equations can be solved by "lifting" from the field Q of rational numbers to an algebraic extension K of Q.

More recently, algebraic number theory has developed into the abstract study of algebraic numbers and number fields themselves, as well as their properties.


See also

Algebraic Extension, Algebraic Integer, Algebraic Number, Class Group, Class Number, Diophantine Equation, Number Field, Number Theory

This entry contributed by David Terr

Explore with Wolfram|Alpha

References

Stewart, I. and Tall, D. Algebraic Number Theory and Fermat's Last Theorem, 3rd ed. Wellesley, MA: A K Peters, 2000.

Referenced on Wolfram|Alpha

Algebraic Number Theory

Cite this as:

Terr, David. "Algebraic Number Theory." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/AlgebraicNumberTheory.html

Subject classifications