This carefully written textbook offers a thorough introduction to abstract algebra, covering the fundamentals of groups, rings and fields. The first two chapters present preliminary topics such as properties of the integers and equivalence relations. The author then explores the first major algebraic structure, the group, progressing as far as the Sylow theorems and the classification of fini…
Daftar isi: BAB 1 Konsep-konsep dasar 1.1 Relasi 1.2 Relasi urutan 1.3 Fungsi 1.4 Pengenalan program GAP (groups, algorithms and programming) BAB 2 Grup 2.1 Operasi 2.2 Grup 2.3 Subgrup 2.4 Grup siklis 2.5 Penggunaan program GAP untuk grup BAB 3 Homomorfisma grup 3.1 Homomorfisma grup 3.2 Subgrup normal dan grup faktor 3.3 Normalisator dan sentralisator 3.4 Penggunaan prog…
Contents: I GROUPS AND SUBGROUPS 1 Introduction and examples 2 Binary operations 3 Isomorphic binary structure 4 Groups 5 Subgroups 6 Cyclic groups 7 Generating sets and cayley digraphs II PERMUTATIONS, COSETS, AND DIRECT PRODUCTS 8 Group of permutations 9 Orbits, cycles and the alternating groups 10 Cosets and the theorem of lagrange 11 Direct products and finitely ge…
Contents: 1. Mappings And Operations 2. Introduction To Groups 3. Equivalence. Congruence. Divisibility 4. Groups 5. Group Homomorphisms 6. Introduction To Rings 7. The Familiar Number R System 8. Polynomials 9. Quotient Rings 10. Galois Theory: Overview 11. Galois Theory 12. Geometric Constructions 13. Geometric Constructions 14. Applications Of Permutation Groups 15. Symmetry …
Contents: 1. GROUPS AND SUBGROUPS 2. PERMUTATIONS, COSETS, AND DIRECT PRODUCTS 3. HOMOMORPHISMS AND FACTOR GROUPS 4. RINGS AND FIELDS 5. IDEALS AND FACTOR RINGS 6. EXTENSION FIELDS 7. ADVANCED GROUP THEORY 8. GROUPS IN TOPOLOGY 9. FACTORYZATION 10. AUTOMORPHISMS AND GALOIS THEORY