Abstract Algebra
Published on 31. August 2004
Book
Hardback
608 pages
978-0-201-70307-8 (ISBN)
Description
A comprehensive undergraduate-level text on abstract algebra, this book allows students to begin their exploration of groups in an environment that is patently non-commutative. Many of the concepts covered in the book can be quickly reviewed in the abstract setting, with the main focus of the review being the differences that arise in the general setting. It is also possible to skip over or delay parts of the first unit. The format of the text assumes that students have already taken an introduction to proofs course and have familiarity with set theory, functions and inductions. It is not assumed that all students have had a course in linear algebra, so the book has included an introduction to vector spaces, bases and linear transformations.
A comprehensive undergraduate-level text on abstract algebra, this book allows students to begin their exploration of groups in an environment that is patently non-commutative. Many of the concepts covered in the book can be quickly reviewed in the abstract setting, with the main focus of the review being the differences that arise in the general setting. It is also possible to skip over or delay parts of the first unit. The format of the text assumes that students have already taken an introduction to proofs course and have familiarity with set theory, functions and inductions. It is not assumed that all students have had a course in linear algebra, so the book has included an introduction to vector spaces, bases and linear transformations.
A comprehensive undergraduate-level text on abstract algebra, this book allows students to begin their exploration of groups in an environment that is patently non-commutative. Many of the concepts covered in the book can be quickly reviewed in the abstract setting, with the main focus of the review being the differences that arise in the general setting. It is also possible to skip over or delay parts of the first unit. The format of the text assumes that students have already taken an introduction to proofs course and have familiarity with set theory, functions and inductions. It is not assumed that all students have had a course in linear algebra, so the book has included an introduction to vector spaces, bases and linear transformations.
More details
Language
English
Place of publication
Harlow
United Kingdom
Publishing group
Pearson Education Limited
Target group
College/higher education
ISBN-13
978-0-201-70307-8 (9780201703078)
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Schweitzer Classification
Person
Content
I Permutations: rigid motions of the square; groups of permutations; cycles and orders; transpositions and an; cycle structure, fixed points and orbits; the cyclic group generated by a permutation; modular arithmetic; matrices and transformations of the plane. II Groups: an axiomatic definition of groups; some properties of groups; subgroups and cyclic groups; conjugation; homomorphisms and isomorphisms; Cosets and Lagranges theorem; normal subgroups and factor groups; vectors and direct products of groups. III Rings and fields: addition and multiplication; rings and some properties; special rings and special elements; new rings from old; polynomial rings; the integers and integral domains; factorization, roots, and ZZx; rings of fractions; vector spaces; polynomials and field extensions. IV Additional topics: finite Abelian groups; group actions and Sylow theorems; unique factorization domains. V Appendices.