Theory of Algebraic Numbers

This book Theory of Algebraic Numbers explains key concepts in algebraic number fields such as their discreteness how polynomials factor valuation theory the unit theorem and the finiteness of class groups along with their proofs. Number theory is useful for constructive mathematics dealing with both discrete and continuous ideas and it reveals hidden challenges in construction. A major part of algebraic number theory involves deciding if a polynomial is irreducible or has a factor a task that is central to many classical explanations. While algebraic number theory might seem straightforward it often involves detailed routines to construct the objects being studied. The book also highlights the early work of researchers who systematically developed the constructive aspects of algebraic number fields.