Cyclic Artinian Modules without a Composition Series

Let R be a ring (always understood to be associative with aunit element 1). It is well known that an R-module is Noetherianif and only if all its submodules are finitely generated andthat it has a finite composition series if and only if it isNoetherian and Artinian. This raises the question whether everyfinitely generated Artinian module is Noetherian; here it isenough to consider cyclic Artinian modules, by an inductionon the length. This question has been answered (negatively)by Brian Hartley [5], who gives a construction of an Artinianuniserial module of uncountable composition-length over thegroup algebra of a free group of countable rank. If we are justinterested in finding cyclic modules that are Artinian but notNoetherian, there is a very simple construction based on thefact that over a free algebra every countably generated Artinianmodule can be embedded in a cyclic module which is again Artinian.This is described in 2 below.     

在乳液体系里制备过氧化氫基聚苯乙烯及其在接枝聚合上的应用

用不同分子量的聚苯乙烯在乳液体系中进行过氧化氢基化反应,然后测定这些产品的特性粘数,HPO值(每1,000个苯乙烯结构单元中所合的过氧化氢基平均数目)等。在过氧化氢基聚苯乙烯的红外光谱里,可以在3,200—3,600厘米~(-1)吸收区里观察到过氧化氢基的吸收带,其吸收强度随着HPO值的增大而加强。最后用这些大分子过氧化物引发甲基丙烯酸甲酯及苯乙烯聚合,得到接枝聚合物。经过分离提纯后,用下列的方法: (1)浊度滴定; (2)热机械性能的测试; (3)水解后测定交换量; (4)红外吸收光谱;证明它们是接枝共聚物。     

Nachweis und Bestimmung einiger Konservierungsmittel in Nahrungsmitteln und Konserven Formaldehyd

Ohne Zusammenfassung     

Eine Bemerkung über die multiplikative Gruppe eines Körpers

Ohne ZusammenfassungHerrnReinhold Baer zum 60. Geburtstag gewidmetThis research was supported by the United States Air Force under Contract No. SAR/G/AF/ OSR/61-29.     

The effect of a carbon-carbon double bond on electron beam-generated plasma decomposition of trichloroethylene and 1,1,1-trichloroethane

The effect of a carbon-carbon double bond on the energy required for decomposition in an electron beam-generated plasma reactor is studied by comparing the decomposition of trichloroethylene and 1,1,1-trichloroethane. A reaction mechanism for TCE decomposition based on a chlorine radical chain reaction is presented which accounts for the formation of all of the experimentally observed reaction products. TCE decomposition is autocatalyzed by reaction products, whereas TCA decomposition is inhibited. The rate expression for the decomposition of TCE in the reactor is determined to be r=−[T](15.07[T₀]^−0.40+0.006{[T₀]−[T]}), where [T] and [T₀] are both in ppm, and r is in ppm Mrad⁻¹. The energy expense ɛ for TCE decomposition is determined as a function of inlet concentration. For 99% decomposition of 100 ppm TCE in air, ɛ=28 eV/molecule, and ɛ=2.5 eV/molecule at 3000 ppm. This is only 2.5–5% of the amount of energy required to decompose a similar amount of TCA as reported by the authors in a previous study. By comparing the energy requirements for TCE decomposition to those for TCA decomposition, the TCE reaction chain length is determined to increase from approximately 20 at 100 ppm initial TCE concentration, to 40 at 3000 ppm. This work was supported by the Contaminant Plume Containment and Remediation Focus Area, Office of Environmental Management, U.S. Department of Energy.     

Spin-state alteration from sterically enforced ligand rotation in bis(indenyl)chromium(II) complexes

The rotational orientation of cyclopentadienyl rings usually has no effect on d-orbital energy levels and splitting in transition metal complexes. With related but less symmetrical carbocyclic ligands, however, the magnetic properties of the associated complexes can be altered by the alignment of the ligands. Examples of this effect are found in substituted organochromium(II) bis(indenyl) complexes. The monosubstituted compounds (1-RC(9)H(6))(2)Cr (R = t-Bu, SiMe(3)) are prepared from the substituted lithium indenides and CrCl(2) in THF; they are high-spin species with four unpaired electrons. Their spin state likely reflects that in the unknown monomeric (C(9)H(7))(2)Cr, which is calculated to have a high-spin (S = 2) ground state in the staggered configuration (180 degrees rotation angle). However, the analogous bis(indenyl) complexes containing t-Bu or SiMe(3) groups in both the 1 and 3 positions on the indenyl ligands ((1,3-R(2)C(9)H(5))(2)Cr) are low-spin compounds with two unpaired electrons. X-ray diffraction results indicate that [1-(t-Bu)C(9)H(6)](2)Cr exists in a staggered conformation, with Cr-C (av) = 2.32(4) A. In contrast, the average Cr-C distances in [1,3-(t-Bu or SiMe(3))(2)C(9)H(5)](2)Cr are 2.22(2) and 2.20(2) A, respectively, and the rings are in a gauche configuration, with rotation angles of 87 degrees. The indenyl conformations are sterically imposed by the bulk of the t-Bu and SiMe(3) substituents. The change from a staggered to a gauche indenyl orientation lowers the symmetry of a (C(9)H(7))(2)M complex and allows greater mixing of metal and ligand orbitals. Calculations indicate that previously nonbonding pi orbitals of the indenyl anion are able to interact with the chromium d orbitals, producing bonding and antibonding combinations. The latter remain unpopulated, and the resulting increase in the HOMO-LUMO gap forces the complexes to adopt a low-spin configuration. The possibility of using sterically imposed ligand rotation as a means of spin-state manipulation makes indenyl compounds a potentially rich source of magnetically adjustable molecules.