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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
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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]).
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- Copyright © Canadian Mathematical Society 1971
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