caa a22 4500 386385297 CHVBK 20180307112056.0 cr unu---uuuuu 161130e198903 xx s 000 0 eng 10.1017/S0305004100067682 doi S0305004100067682 pii (NATIONALLICENCE)cambridge-10.1017/S0305004100067682 Wilson S. M. J. Department of Mathematical Sciences, University of Durham, Durham DHl 3LE The isomorphism class of a set of lattices [Elektronische Daten] [S. M. J. Wilson] Let R be a Dedekind domain with field of quotients K. Let A be a finite-dimensional K-algebra. We consider isomorphism classes and genera in a category whose objects are indexed sets of full R-lattices in some ambient A-module and whose morphisms are the A-homomorphisms of the ambient A-modules which map each lattice into its corresponding lattice. We find conditions under which the stable A-isomorphism class of one particular lattice in an indexed set will determine the stable class of the indexed set within its genus. We apply our methods to show that if L/K is a tame Galois extension of algebraic number fields then the stable isomorphism class of the set of ambiguous ideals in L considered as Galois modules over K is determined by the class of the ring of integers in L together with the inertia subgroups and their standard representations over the respective residue fields of R. Copyright © Cambridge Philosophical Society 1989 Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 105/2(1989-03), 197-210 0305-0041 105:2<197 1989 105 PSP https://doi.org/10.1017/S0305004100067682 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0305004100067682 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Wilson S. M. J. Department of Mathematical Sciences, University of Durham, Durham DHl 3LE NATIONALLICENCE 773 0- Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 105/2(1989-03), 197-210 0305-0041 105:2<197 1989 105 PSP CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge