Certain Number-Theoretic Episodes In Algebra

There are many intersections between the fields of algebra and number theory, and in certain cases there exist explicit algebraic analogues of theorems from number theory.

Presenting the tools needed to explore these linkages, this self-contained reference explains the conceptual foundations of commutative algebra arising from number theory.

Coverage appears in four broad sections, beginning with the elements of number theory and algebra.

The second section details various aspects of algebraic structures with reference to partial ordering and valuation, the third section reviews the fundamentals of algebraic number theory, and the final section explores links involving rings and the Goldbach problem.