Prebasic submodules over valuation rings

Summary Basic concepts in the theory of modules over valuation rings are introduced. The notion of height is used to define indicators of elements, whose irregularities are investigated. The indicator leads to the new notion of smoothness, a property which does not originate from abelian groups. Invariants generalizing the finite Ulm-Kaplansky invariants of abelian p-groups, as well as the Baer invariants for completely decomposable torsion-free abelian groups, are defined, and several results relating these invariants of a module to those of submodules are proved. All these concepts lead to the notion of prebasic submodules, which seems to be the right analogue of the basic subgroups in abelian groups.The authors gratefully acknowledge the support of the National Science Foundation and the Italian C.N.R.     

Temperature distribution and thermal-induced defects in photorefractive barium titanate crystals illuminated with intense cw or pulsed laser irradiations

The temperature distribution in a parallelepipedic crystal irradiated with a Gaussian repartition of light is calculated by solving the three-dimensional heat equation and taking into account the losses through the sides of the samples. The theoretical and experimental maps of temperature are satisfactorily compared. For barium titanate crystals, the resistance to intense cw laser (25.7 kW/mm² at 514.5 nm) and to Nd:YAG pulsed laser (peak power of 9.2 MW at 532 nm) is investigated. The defects induced by the irradiation are analysed. Under pulsed illumination, the damage threshold is found to be 0.54 GW/cm² in a nominally undoped BaTiO₃ and 0.44 GW/cm² in a rhodium-cobalt doped BaTiO₃ crystal. Received: 7 March 2000 / Revised version: 14 April 2000 / Published online: 16 August 2000     

Abelian p-groups with minimal full inertia

Periodica Mathematica Hungarica - The class of abelian p-groups with minimal full inertia, that is, satisfying the property that fully inert subgroups are commensurable with fully invariant...     

Crystal growth and characterization of two-leg spin ladder compounds: Sr14Cu24O41 and Sr2Ca12Cu24O41

Single crystals of Sr_14−xCa_xCu₂₄O₄₁ (x=0 and 12) are grown by the travelling solvent floating zone technique using an image furnace. The grown crystals are characterized for their single crystallinity by the X-ray and Neutron Laue method. The magnetic susceptibility measurements in Sr₁₄Cu₂₄O₄₁ show considerable anisotropy along the main crystallographic axes. Low-temperature specific heat measurement and DC susceptibility measurement in Ca-doped crystal showed antiferromagnetic ordering at 2.8 K at ambient pressure. High-pressure AC susceptibility measurement on Ca-doped crystal showed a sharp superconducting transition at 2 K under 40 kbars. T_c onset reached a maximum value of 9.9 K at 54 kbars. The bulk superconductivity of the sample is confirmed by the high-pressure AC calorimetry with T_c max=9.4 K and T_N=5 K at 56 kbars.     

On finitely injective modules and locally pure-injective modules over Prüfer domains

Over Matlis valuation domains there exist finitely injective modules which are not direct sums of injective modules, as well as complete locally pure-injective modules which are not the completion of a direct sum of pure-injective modules. Over Prüfer domains which are either almost maximal, or -local Matlis, finitely injective torsion modules and complete torsion-free locally pure-injective modules correspond to each other under the Matlis equivalence. Almost maximal Prüfer domains are characterized by the property that every torsion-free complete module is locally pure-injective. It is derived that semi-Dedekind domains are Dedekind.