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R-orders in a Split Algebra have Finitely Many Non-Isomorphic Irreducible Lattices as soon as R has Finite Class Number

Published online by Cambridge University Press:  20 November 2018

Klaus W. Roggenkamp
Klaus W. Roggenkamp*
Affiliation:
McGill University, Montreal, Quebec
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Let R be a Dedekind domain with quotient field K and ∧ an R-order in the finite-dimensional separable K-algebra A. If K is an algebraic number field with ring of integers R, then the Jordan-Zassenhaus theorem states that for every left A-module L, the set SL(M)={M: M=∧-lattice, KM≅L} splits into a finite number of nonisomorphic ∧-lattices (cf. Zassenhaus [5]).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 3 , September 1971 , pp. 405 - 409
Copyright
Copyright © Canadian Mathematical Society 1971

References

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