Introduction to AlgebraThis book is an undergraduate textbook on abstract algebra, beginning with the theories of rings and groups. As this is the first really abstract material students need, the pace here is gentle, and the basic concepts of subring, homomorphism, ideal, etc are developed in detail. Later, asstudents gain confidence with abstractions, they are led to further developments in group and ring theory (simple groups and extensions, Noetherian rings, and outline of universal algebra, lattices and categories) and to applications such as Galois theory and coding theory. There is also a chapteroutlining the construction of the number systems from scratch and proving in three different ways that trascendental numbers exist. |
Other editions - View all
Common terms and phrases
a₁ abelian group addition and multiplication algebraic associative law automorphism axioms binary canonical form closure codewords coefficients column commutative ring complex numbers conjugacy classes construction contains corresponding coset cyclic group define denote det(A divides elementary elements of G entry equal equation equivalence classes equivalence relation Euclidean domain example extension factorisation field F follows function G₁ Galois greatest common divisor group G group of order hence homomorphism induction integral domain inverse irreducible polynomial kernel lattice Let G linearly independent m₁ matrix minimal polynomial module morphisms natural numbers non-zero element normal subgroup notation obtain operation permutation positive integer prime properties Proposition Prove R-module r₁ rational numbers real numbers right cosets ring with identity root of unity satisfies Section splitting field subgroup of G submodule subring subset subspace Suppose symmetric theory unique vector space words zero
References to this book
Oxford Users' Guide to Mathematics Eberhard Zeidler,W. Hackbusch,Hans Rudolf Schwarz No preview available - 2004 |