Perfect rings for which the converse of Schur's lemma holds

If M is a simple module over a ring R then, by the Schur's lemma, the endomorphism ring of M is a division ring. However, the converse of this result does not hold in general, even when R is artinian. In this short note, we consider perfect rings for which the converse assertion is true, and we show that these rings are exactly the primary decomposable ones

The converse of Schur's Lemma in group rings

In this paper, we study the structure of group rings by means of endomorphism rings of their modules. The main tools used here, are the subrings fixed by automorphisms and the converse of Schur's lemma. Some results are obtained on fixed subrings and on primary decomposition of group rings

Mathematical Surfaces and 3D Printing

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Some External Characterizations of SV-Rings and Hereditary Rings

We introduce a new class of rings which we call AI-rings. By applying this property to endomorphism rings, we give characterizations of semi-Artinian V-rings and hereditary rings

Perfect rings for which the converse of Schur's lemma holds

If M is a simple module over a ring R then, by the Schur's lemma, the endomorphism ring of M is a division ring. However, the converse of this result does not hold in general, even when R is artinian. In this short note, we consider perfect rings for which the converse assertion is true, and we show that these rings are exactly the primary decomposable ones

The converse of Schur's Lemma in group rings

In this paper, we study the structure of group rings by means of endomorphism rings of their modules. The main tools used here, are the subrings fixed by automorphisms and the converse of Schur's lemma. Some results are obtained on fixed subrings and on primary decomposition of group rings

Trends in Exercise and Listening Habits of the Sacred Heart University Community

Loud sound levels from the environment can potentially cause permanent damage to the delicate cells inside the hearing organ, the cochlea playing a crucial role in the hearing mechanism. We recommended that trends in exercise and listening habits of the Sacred Heart University community universally change in order to prevent noise-induced hearing loss. Recommendations for safe use of personal listening devices during workouts include keeping volume at a safe level, below 85 dB(A), and limiting time spent using the device during workouts

Effect of BaO-Bi2O3-P2O5 glass additive on structural, dielectric and energy storage properties of BaTiO3 ceramics

International audienceA phosphate BaO-Bi2O3-P2O5 (BBP) glass is added to BaTiO3 ceramics (BT) to investigate its influence on densification, rearrangement of structural units, and dielectric properties of the elaborated composites. The BT ceramic is elaborated by the solid-state method while the glasses BaO-Bi2O3-P2O5 (BBP) are synthesized by the melting-quench process. The synthesized composites are labeled BT-xBBP (x = 2.5, 5, and 7.5 wt %) where x stands for the glass content in weight percent. The density was measured to determine the appropriate sintering temperature of the composites, it was found that the glass addition induces a decrease in their densification and helps their sintering at lower temperatures, the suitable sintering temperature (SST) obtained for all the composites is 900 degrees C. Raman spectroscopy and X-ray Diffraction are performed to study the structural approach of the BBP glass addition to BT ceramics. The scanning electron microscopy was used to examine the morphology of pure BT and sintered composites. It was observed that the BT-(x = 5) composite had a uniform small grains microstructure. The composition dependence of the dielectric properties shows that a material BT-(x = 5) has the highest dielectric constant at room temperature. The P-E plots were carried out and the energy storage parameters (density and efficiency) of the composites are determined. These parameters are affected by the porosity and the remnant polarization of the composites

Structural, optical, and dielectric properties of Bi2O3-K2O-TiO2-P2O5 glasses and related glass-ceramics

International audienceThe glasses in the Bi2O3-K2O-TiO2-P2O5 system were elaborated by the conventional quenching method. Their structure was studied by Raman spectroscopy, and additional information is determined from density measurements and thermal analysis. The optical absorption of the glasses is investigated and it is found that the optical gap and the Urbach energy decrease and increase, respectively, with increasing Bi2O3 content. The crystallization of the glasses was performed under controlled heat treatments to develop glass-ceramics. Their dielectric constants are carried out by impedance spectroscopy. The variations of the permittivity (epsilon(r)) and the dielectric loss (tan delta) versus frequency and temperature are determined. It is evidenced that the introduction of Bi2O3 in the glasses diminished the dispersion at low frequencies. The presence of bismuth oxide in the materials is also beneficial since it allowed the formation of glass-ceramics with high dielectric constant and low dielectric loss