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Course On Abstract Algebra, A (Hardcover, Second Edition)
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Course On Abstract Algebra, A (Hardcover, Second Edition)
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This textbook provides an introduction to abstract algebra for
advanced undergraduate students. Based on the authors' notes at the
Department of Mathematics, National Chung Cheng University, it
contains material sufficient for three semesters of study. It
begins with a description of the algebraic structures of the ring
of integers and the field of rational numbers. Abstract groups are
then introduced. Technical results such as Lagrange's theorem and
Sylow's theorems follow as applications of group theory. The theory
of rings and ideals forms the second part of this textbook, with
the ring of integers, the polynomial rings and matrix rings as
basic examples. Emphasis will be on factorization in a factorial
domain. The final part of the book focuses on field extensions and
Galois theory to illustrate the correspondence between Galois
groups and splitting fields of separable polynomials.Three whole
new chapters are added to this second edition. Group action is
introduced to give a more in-depth discussion on Sylow's theorems.
We also provide a formula in solving combinatorial problems as an
application. We devote two chapters to module theory, which is a
natural generalization of the theory of the vector spaces. Readers
will see the similarity and subtle differences between the two. In
particular, determinant is formally defined and its properties
rigorously proved.The textbook is more accessible and less
ambitious than most existing books covering the same subject.
Readers will also find the pedagogical material very useful in
enhancing the teaching and learning of abstract algebra.
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