Author | Lidl, Rudolf. author |
---|---|
Title | Applied Abstract Algebra [electronic resource] / by Rudolf Lidl, Gรผnter Pilz |
Imprint | New York, NY : Springer US, 1984 |
Connect to | http://dx.doi.org/10.1007/978-1-4615-6465-2 |
Descript | XVIII, 545p. 175 illus. online resource |
1 Lattices -- ยง 1. Properties of Lattices -- ยง2. Boolean Algebras -- ยง3. Minimal Forms of Boolean Polynomials -- Notes -- 2 Applications of Lattices -- ยง1. Switching Circuits -- ยง2. Propositional Logic -- ยง3. Further Applications -- Notes -- 3 Finite Fields and Polynomials -- ยง1. Rings and Fields -- ยง2. Finite Fields -- ยง3. Irreducible Polynomials over Finite Fields -- ยง4. Factorization of Polynomials over Finite Fields -- ยง5. The Nullspace of a Matrix (Appendix to ยง4) -- Notes -- 4 Coding Theory -- ยง1. Linear Codes -- ยง2. Cyclic Codes -- ยง3. Special Cyclic Codes -- Notes -- 5 Further Applications of Fields and Groups -- ยง1. Combinatorial Applications -- ยง2. Algebraic Cryptography -- ยง3. Linear Recurring Sequences -- ยง4. Fast Adding -- ยง5. Polyaโs Theory of Enumeration -- Notes -- 6 Automata -- ยง 1. Semiautomata and Automata -- ยง2. Description of Automata; Examples -- ยง3. Semigroups -- ยง4. Input Sequences -- ยง5. The Monoid of a (Semi-) Automaton and the (Semi-) Automaton of a Monoid -- ยง6. Composition and Decomposition -- ยง7. Minimal Automata -- Notes -- 7 Further Applications of Semigroups -- ยง1. Formal Languages -- ยง2. Semigroups in Biology -- ยง3. Semigroups in Sociology -- 8 Solutions to the Exercises -- 1 -- 2 -- 3 -- 4 -- 5 -- 6 -- 7 -- A. Some Fundamental Concepts -- B. Computer Programs -- Author Index