ABSTRACT

Many basic ideas of algebra and number theory intertwine, making it ideal to explore both at the same time. Certain Number-Theoretic Episodes in Algebra focuses on some important aspects of interconnections between number theory and commutative algebra. Using a pedagogical approach, the author presents the conceptual foundations of commutati

part |2 pages

Part I - ELEMENTS OF NUMBER THEORY AND ALGEBRA

chapter 1|26 pages

Theorems of Euler, Fermat and Lagrange

chapter 2|18 pages

The integral domain of rational integers

chapter 3|26 pages

Euclidean domains

chapter 6|38 pages

Reciprocity laws

chapter 7|26 pages

Finite groups

part |2 pages

Part II: THE RELEVANCE OF ALGEBRAIC STRUCTURES TO NUMBER THEORY

part |2 pages

Part III - A GLIMPSE OF ALGEBRAIC NUMBER THEORY

chapter 12|60 pages

Noetherian and Dedekind domains

chapter 13|46 pages

Algebraic number fields

part |2 pages

Part IV - SOME MORE INTERCONNECTIONS

chapter 14|42 pages

Rings of arithmetic functions

chapter 15|52 pages

Analogues of the Goldbach problem

chapter 16|38 pages

An epilogue: More interconnections