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Books > Science & Mathematics > Mathematics > Algebra
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Introduction To Abstract Algebra, An: Sets, Groups, Rings, And Fields (Hardcover)
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Introduction To Abstract Algebra, An: Sets, Groups, Rings, And Fields (Hardcover)
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This book is a textbook for a semester-long or year-long
introductory course in abstract algebra at the upper undergraduate
or beginning graduate level.It treats set theory, group theory,
ring and ideal theory, and field theory (including Galois theory),
and culminates with a treatment of Dedekind rings, including rings
of algebraic integers.In addition to treating standard topics, it
contains material not often dealt with in books at this level. It
provides a fresh perspective on the subjects it covers, with, in
particular, distinctive treatments of factorization theory in
integral domains and of Galois theory.As an introduction, it
presupposes no prior knowledge of abstract algebra, but provides a
well-motivated, clear, and rigorous treatment of the subject,
illustrated by many examples. Written with an eye toward number
theory, it contains numerous applications to number theory
(including proofs of Fermat's theorem on sums of two squares and of
the Law of Quadratic Reciprocity) and serves as an excellent basis
for further study in algebra in general and number theory in
particular.Each of its chapters concludes with a variety of
exercises ranging from the straightforward to the challenging in
order to reinforce students' knowledge of the subject. Some of
these are particular examples that illustrate the theory while
others are general results that develop the theory further.
General
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