The genus of a module |
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Authors: | Robert M Guralnick |
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Institution: | Department of Mathematics, University of Southern California, Los Angeles, California 90089 USA |
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Abstract: | Let R be a Dedekind domain satisfying the Jordan-Zassenhaus theorem (e.g., the ring of integers in a number field) and Λ a module finite R-algebra. We extend classical results of Jacobinski, Roiter, and Drozd on orders and lattices. In particular, it is shown that the genus of a finitely generated Λ-module M is finite. Moreover, given M, there exist a positive integer t and a finite extension S of R such that a Λ-module N is the genus of M if and only if M(t) ? N(t) if and only if M ? S ? N ? S. |
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