The Hausdorff Completion of the Space of Closed Subsets of a Module
Canadian mathematical bulletin, Tome 38 (1995) no. 3, pp. 325-329
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In this paper, we show that the lattice of closed subsets of the completion, in the Jacobson radical topology, of a finitely generated module M is isomorphic to the completion, under the Hausdorff topology, of the lattice of closed subsets of M. This extends submodule-theoretic results for complete modules to modules satisfying Chevalley's Theorem. We show that the lattice of submodules of every finitely generated module over a semi-local ring R is complete in the Hausdorff topology if and only if R is complete in the Jacobson radical topology.
Johnson, E. W.; Johnson, Johnny A. The Hausdorff Completion of the Space of Closed Subsets of a Module. Canadian mathematical bulletin, Tome 38 (1995) no. 3, pp. 325-329. doi: 10.4153/CMB-1995-047-4
@article{10_4153_CMB_1995_047_4,
author = {Johnson, E. W. and Johnson, Johnny A.},
title = {The {Hausdorff} {Completion} of the {Space} of {Closed} {Subsets} of a {Module}},
journal = {Canadian mathematical bulletin},
pages = {325--329},
year = {1995},
volume = {38},
number = {3},
doi = {10.4153/CMB-1995-047-4},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1995-047-4/}
}
TY - JOUR AU - Johnson, E. W. AU - Johnson, Johnny A. TI - The Hausdorff Completion of the Space of Closed Subsets of a Module JO - Canadian mathematical bulletin PY - 1995 SP - 325 EP - 329 VL - 38 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1995-047-4/ DO - 10.4153/CMB-1995-047-4 ID - 10_4153_CMB_1995_047_4 ER -
%0 Journal Article %A Johnson, E. W. %A Johnson, Johnny A. %T The Hausdorff Completion of the Space of Closed Subsets of a Module %J Canadian mathematical bulletin %D 1995 %P 325-329 %V 38 %N 3 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1995-047-4/ %R 10.4153/CMB-1995-047-4 %F 10_4153_CMB_1995_047_4
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