This article is cited in 2 papers

Modules lattice isomorphic to linearly compact modules

G. M. Brodskii

P. G. Demidov Yaroslavl State University

Abstract: We study modules that are lattice isomorphic to linearly compact modules (in the discrete topology). In particular, we establish the equivalence of the following properties of a module $M$: 1) $M$ satisfies the Grothendieck property \textrm{AB$5^*$} and all its submodules are Goldie finite-dimensional; 2) $M$ is lattice isomorphic to a linearly compact module; 3) $M$ is lattice antiisomorphic to a linearly compact module. We show that a linearly compact module cannot be determined in terms of the lattice of its submodules.

UDC: 512.553

Received: 19.09.1994

DOI: 10.4213/mzm1704

 English version: Mathematical Notes, 1996, 59:2, 123–127

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