Background material on rings and modules -- Modules over commutative rings -- The Wedderburn-Artin Theorem -- Separable Algebras, definition and first properties -- Exercises -- Background material on homological algebra -- The divisor class group -- Azumaya algebras -- derivations, differentials and separability -- Etale algebras -- Henselization and splitting rings -- Galois extensions of commutative rings -- Crossed products and galois cohomology -- Further topics.
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TOPICAL NAME USED AS SUBJECT
Associative rings, Textbooks
Separable algebras, Textbooks
Algebraic geometry-- (Colo.)homology theory-- Étale and other Grothendieck topologies and (co)homologies.
Algebraic geometry-- Local theory-- Local structure of morphisms: Étale, flat, etc.
Associative rings and algebras-- Algebras and orders-- Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)
Associative rings and algebras-- Instructional exposition (textbooks, tutorial papers, etc.)
Associative rings.
Commutative algebra-- General commutative ring theory-- Ideals; multiplicative ideal theory.