Author | Adkins, William A. author |
---|---|
Title | Algebra [electronic resource] : An Approach via Module Theory / by William A. Adkins, Steven H. Weintraub |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1992 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0923-2 |
Descript | X, 526 p. online resource |
1 Groups -- 1.1 Definitions and Examples -- 1.2 Subgroups and Cosets -- 1.3 Normal Subgroups, Isomorphism Theorems, and Automorphism Groups -- 1.4 Permutation Representations and the Sylow Theorems -- 1.5 The Symmetric Group and Symmetry Groups -- 1.6 Direct and Semidirect Products -- 1.7 Groups of Low Order -- 1.8 Exercises -- 2 Rings -- 2.1 Definitions and Examples -- 2.2 Ideals, Quotient Rings, and Isomorphism Theorems -- 2.3 Quotient Fields and Localization -- 2.4 Polynomial Rings -- 2.5 Principal Ideal Domains and Euclidean Domains -- 2.6 Unique Factorization Domains -- 2.7 Exercises -- 3 Modules and Vector Spaces -- 3.1 Definitions and Examples -- 3.2 Submodules and Quotient Modules -- 3.3 Direct Sums, Exact Sequences, and Horn -- 3.4 Free Modules -- 3.5 Projective Modules -- 3.6 Free Modules over a PID -- 3.7 Finitely Generated Modules over PIDs -- 3.8 Complemented Submodules -- 3.9 Exercises -- 4 Linear Algebra -- 4.1 Matrix Algebra -- 4.2 Determinants and Linear Equations -- 4.3 Matrix Representation of Homomorphisms -- 4.4 Canonical Form Theory -- 4.5 Computational Examples -- 4.6 Inner Product Spaces and Normal Linear Transformations -- 4.7 Exercises -- 5 Matrices over PIDs -- 5.1 Equivalence and Similarity -- 5.2 Hermite Normal Form -- 5.3 Smith Normal Form -- 5.4 Computational Examples -- 5.5 A Rank Criterion for Similarity -- 5.6 Exercises -- 6 Bilinear and Quadratic Forms -- 6.1 Duality -- 6.2 Bilinear and Sesquilinear Forms -- 6.3 Quadratic Forms -- 6.4 Exercises -- 7 Topics in Module Theory -- 7.1 Simple and Semisimple Rings and Modules -- 7.2 Multilinear Algebra -- 7.3 Exercises -- 8 Group Representations -- 8.1 Examples and General Results -- 8.2 Representations of Abelian Groups -- 8.3 Decomposition of the Regular Representation -- 8.4 Characters -- 8.5 Induced Representations -- 8.6 Permutation Representations -- 8.7 Concluding Remarks -- 8.8 Exercises -- Index of Notation -- Index of Terminology