Theoretical Concept of Algebraic Number Theory |

ABSTRACT:

In this paper we present about theoretical concept of algebraicnumber theory. Algebraic number theory studies algebraic properties of the ringof algebraic integers in a number field. We describe various algebraicinvariants of number fields, as well as their applications. These applicationsrelate to prime ramification, the finiteness of the class number, cyclotomicextensions, and the unit theorem.