Lifting Isomorphisms of Modules
Canadian journal of mathematics, Tome 31 (1979) no. 4, pp. 808-811
Voir la notice de l'article provenant de la source Cambridge University Press
Throughout this note, let R be a discrete valuation ring with prime element π, residue class field , and quotient field K. Let Λ be an R-order in a finite dimensional K-algebra A. A Λ-lattice is an R-free finitely generated left Λ-module. For k > 0, we set where M is any Λ-lattice. Obviously, for Λ-lattices M and N, Maranda [1] and D. G. Higman [3] considered the reverse implication, and ProvedTHEOREM. Let Λ be an R-order in a separable K-algebra A. Then there exists a positive integer k (which depends on Λ) with the following property: for each pair of Λ-lattices M and N, Indeed,m it suffices to choose k so that Maranda proved this result for the special case where Λ is the integral group ring RG of a finite group G.
Reiner, Irving. Lifting Isomorphisms of Modules. Canadian journal of mathematics, Tome 31 (1979) no. 4, pp. 808-811. doi: 10.4153/CJM-1979-074-2
@article{10_4153_CJM_1979_074_2,
author = {Reiner, Irving},
title = {Lifting {Isomorphisms} of {Modules}},
journal = {Canadian journal of mathematics},
pages = {808--811},
year = {1979},
volume = {31},
number = {4},
doi = {10.4153/CJM-1979-074-2},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1979-074-2/}
}
[1] 1. Maranda, J. M., On p-adic integral representations of finite groups, Can. J. Math. 5 (1953), 344–355. Google Scholar
[2] 2. Curtis, C. W. and Reiner, I., Representation theory of finite groups and associative algebras (Wiley and Sons, New York, 1962). Google Scholar
[3] 3. Higman, D. G., On representations of orders over Dedekind domains, Can. J. Math. 12 (1960), 107–125. Google Scholar
Cité par Sources :