Algebra: v. 3

Part 1 Universal algebra: algebras and homomorphisms; congruences and the isomorphism theorems; free algebrae and varieties; abstract dependence relations; the diamond lemma; ultraproducts; the natural numbers. Part 2 Multilinear algebra: graded algebras; free algebras and tensor algebras; the hilbert series of a graded algebra or module; the exterior algebra on a module. Part 3 Homological algebra: additive and abelian categories; functors on abelian categories; homological dimension. Part 4 Further group theory: group extensions; the Frattini subgroup and the pitting subgroup; free groups; linear groups. Part 5 Further field theory: algebraic dependence; derivations; infinite algebraic extensions; Galois cohomology. Part 6 Algebras: the Frull-Schmidt theorem; semiperfect rings; the Morita context; Fochschild cohomology and separable algebras. Part 7 Central simple algebras: the Brauer group; charge of base field; cyclic algebras. Part 8 Quadratic forms and ordered fields: the Clifford algebra of a quadratic space; the Witt ring of a field; the symplectic group; the orthogonal group. Part 9 Koetherian rings and polynomial identities: rings of fractions; skew polynomials and Laurent series; Goldie's theorem; PJ-algebras; generic metrix rings and central polynemials; generalized polynomial identities. Part 10 Rings without finitensee assumptions: the endemorphism ring of a vector space; primitive rings; semiprimitive rings and the Jacobeon radical; algebras without a unit element. Part 11 Skew fields: the Dieudonne determinant; pseudo-linear extensions.