Monogenous algebras. Back to Kronecker.

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.
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Submitted on : Friday, October 17, 2003 - 11:07:10 AM
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Daniel Ferrand. Monogenous algebras. Back to Kronecker.. Note écrite en septembre 2003. 13 pages. 2003. 〈hal-00000740〉

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