Discrete valuation domains and ranks of their maximal extension
Commutative domains large in their -adic completions
Abelian groups of zero adjoint entropy
The notion of adjoint entropy for endomorphisms of an Abelian group is somehow dual to that of algebraic entropy. The Abelian groups of zero adjoint entropy, i.e. ones whose endomorphisms all have zero adjoint entropy, are investigated. Torsion groups and cotorsion groups satisfying this condition are characterized. It is shown that many classes of torsionfree groups contain groups of either zero or infinite adjoint entropy. In particular, no characterization of torsionfree groups of zero adjoint...
Fully inert submodules of torsion-free modules over the ring of p-adic integers
Fully inert submodules of torsion-free -modules are investigated. It is proved that if the module considered is either free or complete, these submodules are exactly those which are commensurable with fully invariant submodules; examples are given of torsion-free -modules for which this property fails.
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