Strongly Gorenstein projective, injective, and flat modules

In this paper, we study a particular case of Gorenstein projective, injective, and flat modules, which we call, respectively, strongly Gorenstein projective, injective, and flat modules. These last three classes of modules give us a new characterization of the first modules, and confirm that there is an analogy between the notion of “Gorenstein projective, injective, and flat modules” and the notion of the usual “projective, injective, and flat modules”.     

Wastewater treatment using gamma irradiation: Tétouan pilot station,Morocco

The increasing demand on limited water supplies has accelerated the wastewater reuse and reclamation. We investigated gamma irradiation effects on wastewater by measuring differences in the legislated parameters, aiming to reuse the wastewater. Effluents samples were collected at the urban wastewater treatment station of Tetouan and were irradiated at different doses ranging from 0 to 14 kGy using a Co⁶⁰ gamma source. The results showed an elimination of bacterial flora, a decrease of biochemical and chemical oxygen demand, and higher conservation of nutritious elements. The results of this study indicated that gamma irradiation might be a good choice for the reuse of wastewater for agricultural activities.     

4-Ammonio-2,2,6,6-tétraméthylpipéridinium chromate dihydrate

The title compound, 4-ammonio-2,2,6,6-tetramethyl­piperi­dinium chromate dihydrate, (C₉H₂₂N₂)[CrO₄]·2H₂O, crystallizes in the monoclinic system with one organic cation and one chromate anion in the asymmetric unit, together with three independent sites for water molecules, two of which have their O atoms located on twofold axes. The structure is composed of layers built up from CrO₄²⁻ tetrahedra and water molecules alternating with C₉H₂₂N₂²⁺ cations and additional water molecules. Two types of hydrogen bonds, O—H⋯O and N—H⋯O, ensure the cohesion and stability of the structure.     

Crystal structure of bis 4-benzyl piperidinium monohydrogenmonophosphate pentahydrate, [C6H5CH2CHCH2CH2NH2CH2CH2]2HPO4·5H2O

The salt bis 4-benzyl piperidinium monohydrogenmonophosphate pentahydrate is orthorhombic with the following unit cell dimensions: a = 11.235(2) Å, b = 27.924(6) Å, c = 9.321(4) Å space group Pca2₁ with Z = 4. The structure was solved by the Patterson method and refined to final R value of 0.049 for 1802 independent reflections. The flack parameter is 0.14 with an e.s.d. of 0.23. The structure consists of infinite parallel two-dimensional [110] planes built of mutually connected ions and water molecules by strong O—H,...,O and N—H,...,O hydrogen bonding. There are no contacts other than normal van der Waals interactions between the layers.     

Sur le groupe des classes d'un anneau intègre

In this paper, we are interested in a generalization of Nagata's theorem [13] to a new class of domains other than Krull domains, the Mori domains and the PVMD domains (Theorem 1).