Lecture Notes in Mathematics

By: R. Sot

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Paperback | 1 July 1982

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156 Pages

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The Zariski topology, the Jacobian criterion and examples of simple algebras over a field k.- The Kahler 1-differentials.- Every k-algebra a which is essentially of finite type over k and simple is a regular local ring.- Brief discussion of unramified and etale homomorphisms.- Some corollaries to Theorem 3.5.- Fitting ideals.- Proof of the Jacobian criterion and some characterizations of simple k-algebras and A-algebras.- Characterizations of simple A-algebras in terms of etale homomorphisms; invariance of the property of being a simple algebra under composition and change of base.- Descent of simple homomorphisms and removal of all noetherian assumptions in Chapter 7 and Chapter 8.- Simple morphisms of preschemes and translation of previous theorems into the language of preschemes.

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