Abstract Algebra 3rd Edition, David S. Dummit , Richard M. Foote

 Abstract Algebra  3rd Edition, David S. Dummit  , Richard M. Foote 

    A basic introductory (one year) course should probably include Part I up through Section 5.3, Part II through Section 9.5, Sections 10.1, 10.2, 10.3, 11.1, 11.2 and Part IV. Chapter 12 should also be covered, either before or after Part IV. Additional topics from Chapters 5, 6, 9, 10 and 11 may be interspersed in such a course, or covered at the end as time permits. 

    Sections 10.4 and 10.5 are at a slightly higher level of difficulty than the initial sections of Chapter 10, and can be deferred on a first reading for those following the text sequentially. The latter section on properties of exact sequences, although quite long, maintains coherence through a parallel treatment of three basic functors in respective subsections. 

    Beyond the core material, the third edition provides significant flexibility for stu dents and instructors wishing to pursue a number of important areas of modem algebra,either in the form of independent study or courses. For example, well integrated one s emester courses for students with some prior algebra background might include the following: Section 9.6 and Chapters 15 and 16; or Chapters 10 and 17; or Chapters 5, 6 and Part VI. Each of these would also provide a solid background for a follow-up c ourse delving more deeply into one of many possible areas: algebraic number theory, a lgebraic topology, algebraic geometry, representation theory, Lie groups, etc. 

Topics are devided 6 part, they are

Part 1-GROUP THEORY 

Part II -RING THEORY 

Part Ill -MODULES AND VECTOR SPACES

Part IV-FIELD THEORY AND GALOIS THEORY 

Part V-AN INTRODUCTION TO COMMUTATIVE RINGS, ALGEBRAIC GEOMETRY, AND HOMOLOGICAL ALGEBRA 

Part VI -INTRODUCTION TO THE REPRESENTATION THEORY OF FINITE GROUPS 

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