Certain Number-Theoretic Episodes In AlgebraCRC Press, 22 sept. 2006 - 632 pages 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 |
Table des matières
Theorems of Euler Fermat and Lagrange | 3 |
The integral domain of rational integers | 29 |
Euclidean domains | 47 |
Rings of polynomials and formal power series | 73 |
The Chinese Remainder Theorem and the evaluation of number of solutions of a linear congruence with side conditions | 105 |
Reciprocity laws | 139 |
Finite groups | 177 |
THE RELEVANCE OF ALGEBRAIC STRUCTURES TO NUMBER THEORY | 203 |
A GLIMPSE OF ALGEBRAIC NUMBER THEORY | 373 |
Noetherian and Dedekind domains | 375 |
Algebraic number fields | 435 |
SOME MORE INTERCONNECTIONS | 481 |
Rings of arithmetic functions | 483 |
Analogues of the Goldbach problem | 525 |
An epilogue More interconnections | 577 |
BIBLIOGRAPHY | 615 |
Ordered fields fields with valuation and other algebraic structures | 205 |
The role of the Möbius function Abstract Möbius inversion | 261 |
The role of generating functions | 291 |
Semigroups and certain convolution algebras | 339 |
Autres éditions - Tout afficher
Certain Number-Theoretic Episodes In Algebra Sivaramakrishnan R,R Sivaramakrishnan Aperçu limité - 2006 |
Expressions et termes fréquents
addition algebra Applied arithmetic functions associated assume basis belongs called chapter character coefficients commutative ring complex condition congruence consider contains Corollary corresponding cyclic Dedekind domain defined Definition denotes direct Dirichlet distinct divides division divisors element equal equation example exists expressed extension Fact factors field finite follows Further given gives holds homomorphism identity infinite integral domain Introduction inverse isomorphic known lattice least lemma linear Math matrix maximal ideal modulo multiplication Noetherian nonzero norm normal number field number theory observe obtain otherwise polynomial positive integer primary prime ideal principal ideal Proof proper prove quadratic rational relation Remark representation residue satisfies semigroup shown solution squares subgroup subset Suppose theorem unique unit unity vector space write zero