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1 IRMAR - Institut de Recherche Mathématique de Rennes

Abstract : In this note we develop some properties of those algebras called here locally simple which can be generated by a single element after, if need be, a faithfullyflat extension. For finite algebras, this is shown to be in fact a property of the geometric fibers. Morphisms between rings of algebraic integersare locally simple. Expanding an idea introduced by Kronecker we show that much ofthe properties in particular local simplicity of a finite and locally free A-algebra B can be read through the characteristic polynomial of the generic element of B.

Autor: Daniel Ferrand -



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