The companion title, Linear Algebra, has sold over 8,000 copies
The writing style is very accessible
The material can be covered easily in a one-year or one-term course
Includes Noah Snyder's proof of the Mason-Stothers polynomial abc theorem
New material included on product structure for matrices including descriptions of the conjugation representation of the diagonal group
Rezensionen / Stimmen
From the reviews of the third edition: "As is very typical for Professor Lang's self demand and style of publishing, he has tried to both improve and up-date his already well-established text. ... Numerous examples and exercises accompany this now already classic primer of modern algebra, which as usual, reflects the author's great individuality just as much as his unrivalled didactic mastery and his care for profound mathematical education at any level. ... The present textbook ... will remain one of the great standard introductions to the subject for beginners." (Werner Kleinert, Zentralblatt MATH, Vol. 1063, 2005)
Reihe
Auflage
Sprache
Verlagsort
Zielgruppe
Für Beruf und Forschung
Research
Illustrationen
1
1 farbige Abbildung
1 colour illustrations, biography
Maße
Gewicht
ISBN-13
978-0-387-96404-1 (9780387964041)
DOI
10.1007/978-1-4684-9234-7
Schweitzer Klassifikation
I The Integers.- §1. Terminology of Sets.- §2. Basic Properties.- §3. Greatest Common Divisor.- §4. Unique Factorization.- §5. Equivalence Relations and Congruences.- II Groups.- §1. Groups and Examples.- §2. Mappings.- §3. Homomorphisms.- §4. Cosets and Normal Subgroups.- §5. Permutation Groups.- §6. Cyclic Groups.- §7. Finite Abelian Groups,.- III Rings.- §1. Rings.- §2. Ideals.- §3. Homomorphisms.- §4. Quotient Fields.- IV Polynomials.- §1. Euclidean Algorithm.- §2. Greatest Common Divisor.- §3. Unique Factorization.- §4. Partial Fractions.- §5. Polynomials over the Integers.- §6. Transcendental Elements.- §7. Principal Rings and Factorial Rings.- V Vector Spaces and Modules.- §1. Vector Spaces and Bases.- §2. Dimension of a Vector Space.- §3. Matrices and Linear Maps.- §4. Modules.- §5. Factor Modules.- §6. Free Abelian Group.- VI Some Linear Groups.- §1. The General Linear Group.- §2. Structure of GL2(F).- §3. SL2(F).- VII Field Theory.- §1. Algebraic Extensions.- §2. Embeddings'.- §3. Splitting Fields'.- §4. Galois Theory.- §5. Quadratic and Cubic Extensions.- §6. Solvability by Radicals.- §7. Infinite Extensions.- VIII Finite Fields.- §1. General Structure.- §2. The Frobenius Automorphism.- §3. The Primitive Elements.- §4. Splitting Field and Algebraic Closure.- §5. Irreducibility of the Cyclotomic Equation over Q.- §6. Where Does It All Go? Or Rather, Where Does Some of It Go?.- IX The Real and Complex Numbers.- §1. Ordering of Rings.- §2. Preliminaries.- §3. Construction of the Real Numbers.- §4. Decimal Expansions.- §5. The Complex Numbers.- X Sets.- §1. More Terminology.- §2. Zona's Lemma.- §3. Cardinal Numbers.- §4. Well-ordering.- §1. The Natural Numbers.- §2. The Integers.- §3. Infinite Sets.
