Subalgebras that are cyclic as submodules

Let R be an associative, commutative, unital ring. By a R-algebra we mean a unital R-module A together with a R-module homomorphism : _R ⁿ AA (n2). We raise the question whether such an algebra possesses either an idempotent or a nilpotent element. In section 1 an affirmative answer is obtained in case R=k is an algebraically closed field and dim_kA<, as well as in case R=, dimS<, and n0(2). Section 2 deals with the case of reduced rings R and R-algebras which are finitely generated and projective as R-modules. In section 3 we show that the generic algebra over an integral domain D fails to have nilpotent elements in any integral domain extending its base ring D_n,m, and thus acquires an idempotent element in some integral domain extending D_n,m.Partially supported by National Science Foundation Grant GP-38229.     

On purely radiative space-times

The existence of space-times representing pure gravitational radiation which comes in from infinity and interacts with itself is discussed. They are characterized as solutions of Einstein's vacuum field equations possessing a smooth structure at past null infinity which forms the future null cone at past timelike infinity with complete generators. The pure radiation problem is analysed where free initial data for Einstein's field equations are prescribed on the null cone at past time-like infinity. It is demonstrated how the pure radiation problem can be formulated as a local initial value problem for the symmetric hyperbolic system of reduced conformal vacuum field equations. Its solutions are uniquely determined by the free data.Work supported by a Heisenberg-fellowship of the Deutsche Forschungsgemeinschaft     

Decomposition of neutral, singly and doubly protonated benzoquinone in the gas phase

The unimolecular fragmentations of singly and doubly protonated ortho-, meta-, and para-benzoquinones (BQH(+) and BQH(2)(2+), respectively) are studied by tandem mass spectrometry. The dominant fragmentation pathways lead to the elimination of a neutral CO molecule from BQH(+) and, by charge separation, to the expulsion of protonated CO from BQH(2)(2+). Reaction mechanisms are elucidated based on labeling experiments and UB3 LYP calculations. These results reveal that the respective reactions proceed in an analogous fashion to the decarbonylation of neutral benzoquinones, which decompose into carbon monoxide and cyclopentadienone. Single protonation facilitates all steps on the reaction pathway with neutral CO and O-protonated cyclopentadienone as final products. In contrast, double protonation leads to an increase of the barriers for the decomposition yielding CO.H(+) and O-protonated cyclopentadienone. This major process of BQH(2)(2+) is accompanied by two minor channels, which lead to the elimination of neutral carbon monoxide and water, respectively. The proton affinity of the para-BQH(+) monocation is estimated as 3.6+/-0.3 eV.     

Diastereoselective Synthesis of <Emphasis Type="Italic">cis</Emphasis>-2,6-Disubstituted Perhydro-4-pyranones Using Elevated Pressure Hydrogenation

Summary. A diastereoselective strategy for the synthesis of γ-pyrons was developed, starting from the Mg diacetonedicarboxylate complex. Initial cyclization with suitable anhydrides or acid chlorides, followed by hydrolytic decarboxylation leads to 2,6-disubstituted pyrans. Elevated pressure hydrogenation using Pd/C affords the title compounds in high diastereoselectivity. Scope and limitations of the method are outlined on selected examples.     

Vertauschbarkeit von Limites und Colimites

We characterize the pairs (A,B) of small categories having the property thatA ^op-limits andB-colimits commute inSets. A necessary condition on such pairs is thatB be filtered with respect to diagrams of typeA. This condition, however, is far from being sufficient. ForA a discrete category, products of typeA andB-colimits commute inSets iffB is filtered with respect to diagrams of typeA and, providedA is infinite, additionally with respect to diagrams of type ···. In particular,B-colimits commuting with denumerable products commute with equalizers, too. ForA a connected category,A ^op-limits andB-colimits commute inSets iff the completion ofB under some set of connected limits is filtered with respect to diagrams of typeA. Since discrete limits and connected limits suffice, the characterization is complete.We apply our characterization to particular choices forA and conclude with a complete list of the regular classes of colimits in the sense of Gabriel and Ulmer.     

Über neue olefin-dicarbonyl-isonitril-eisen(0)-komplexe

The reactions of [R₃O]BF₄ or R₃ECl (R = Me, Et; E = Si, Ge, Sn, Pb) with various olefincyanodicarbonyl ferrates(0) [olenFe(CO)₂CN]^?] (olen  C₄H₆, C₅H₈, C₆H₈, C₆H₁₀, C₇H₁₀, C₈H₈, C₈H₁₄), which can be easily synthesized from olenFe(CO)₃ and NaN(SiMe₃)₂, lead to the neutral isonitrile derivatives olenFe(CO)₂CNR or olenFe(CO)₂CNER₃. The 31 new complexes are characterized by their analyses, IR and ¹H NMR spectra.     

Zur Kinetik des durch Cu2+-Äthylendiamin katalysierten H2O2-Zerfalls: Metallionen und H2O2, 14. Mitteilung

Kinetic studies of the Cu²⁺-ethylenediamine catalysed decomposition of H₂O₂ show the initial rate v₀ of H₂O₂ decomposition to be proportional to [H+]^?1, [H₂O₂], and [Cu²⁺-en]². Maximal velocity is found at a ratio of [Cu²⁺]_tot:[en]_tot = 1:1,5. It is suggested that the active complex has a binuclear structure. This structure and probable mechanisms of the reaction are discussed. The kinetic measurements of the Cu²⁺-diethylenetriamine-H₂O₂ system are difficult to interprete because of degradation of the ligand by H₂O₂.     

Synthesis of nanosized BaSnO3 powders from metal isopropoxides

Nanocrystalline BaSnO₃ with a primary particle size of 40–60 nm was prepared through hydrolysis of a barium tin isopropoxide and following crystallization. The thermal decomposition, the crystallization and the microstructure of the obtained powders were investigated with the help of TG-DTA, IR, XRD, HRSEM and HRTEM. The organic rest groups in the as-prepared powder decompose thermally at 350°C, which is accompanied by the building of BaCO₃ that disappear again at 600°C. The crystallization of BaSnO₃ takes place at 500–600°C. Single-phase BaSnO₃ powders have been obtained at a temperature as low as 600°C. The amorphous as-prepared powder shows a cluster structure. Nucleation of BaSnO₃ beginning at 350°C was observed under HRTEM, and the spherical nano-particles of BaSnO₃ calcined at 760°C crystallize well and are strongly aggregated. The presented results indicate a heterogeneous nucleation and growth mechanism by the formation of BaSnO₃.     

The crystal and molecular structure of tris(ortho-aminobenzoato)aquoyttrium(III), Y(H2NC6H4COO)3 · H2O

Tris(ortho-aminobenzoato)aquoyttrium(III), Y(H₂NC₆H₄COO)₃ · H₂O, crystallizes in the monoclinic space group, $\text{C2}\text{c}$, with eight molecules in a unit cell of dimensions: a = 30.89(1) Å, b = 9.09(1) Å, c = 14.85(1) Å, and β = 109.3(1)°. The structure was determined using three-dimensional X-ray diffraction data gathered on multiple-film equi-inclination, integrated Weissenberg, and precession photographs taken about two crystal axes. The structure, excluding the hydrogen atoms, was solved from Patterson and electron density maps and refined by least-squares methods to a final R of 0.081. The coordination about the yttrium atom is sevenfold, best described by a capped trigonal prism. Each ortho-aminobenzoate ligand acts as a bridging bidentate ligand, resulting in six ortho-aminobenzoate residues coupled to each yttrium atom. The water molecule occupies the seventh position. This bonding configuration generates a structure in which each yttrium atom in (100) is attached to two other yttrium atoms via carboxylate bridges to give parallel sets of polymeric chains coincident with (100). It is suggested that this polymeric character accounts for the extreme insolubility of Y(H₂NC₆H₄COO)₃ · H₂O.