A Book of Abstract Algebra: Second Edition
Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. Intended for undergraduate courses in abstract algebra, it is suitable for junior- and senior-level math majors and future math teachers. This second edition features additional exercises to improve student familiarity with applications.
An introductory chapter traces concepts of abstract algebra from their historical roots. Succeeding chapters avoid the conventional format of definition-theorem-proof-corollary-example; instead, they take the form of a discussion with students, focusing on explanations and offering motivation. Each chapter rests upon a central theme, usually a specific application or use. The author provides elementary background as needed and discusses standard topics in their usual order. He introduces many advanced and peripheral subjects in the plentiful exercises, which are accompanied by ample instruction and commentary and offer a wide range of experiences to students at different levels of ability.
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abelian group automorphism called Chapter closed with respect codeword coefﬁcients commutative ring congruences constructible contains coset cyclic group deﬁned deﬁnition denote divisors of zero element of G element of order equal equation equivalence relation example Exercise Explain extension of F factor ﬁeld F ﬁnd ﬁnite extension ﬁnite group ﬁrst ﬁxed function f Galois group gcd(a group G hence HINT homomorphic image ideal identity element inﬁnite integral domain inverse irreducible polynomial isomorphism kernel lemma Let F Let G Let H linear combination mathematics matrix modulo normal subgroup nth roots number of elements operation partition permutation polynomial a(x polynomial of degree positive integer prime number proof properties Prove that G Prove the following quotient group quotient ring real numbers relatively prime ring with unity root ﬁeld roots of a(x satisﬁes solution solvable solve subgroup of G subring subset Suppose surjective Theorem vector space