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The lattice of fully invariant submodules of a reduced cotorsion \(p\)-adic module. (English) Zbl 1230.20052

Summary: The paper considers the lattice of fully invariant submodules of a reduced cotorsion \(p\)-adic module \(T^*\oplus C\), where \(T\) is a countable direct sum of torsion-complete \(p\)-groups and \(C\) is a torsion-free, algebraically compact group. It is shown that this lattice is isomorphic to a lattice of filters of a semilattice made up of infinite matrices and indicators.

MSC:

20K27 Subgroups of abelian groups
13C13 Other special types of modules and ideals in commutative rings
20E15 Chains and lattices of subgroups, subnormal subgroups
20K21 Mixed groups
20K10 Torsion groups, primary groups and generalized primary groups
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