Rings Over Which Cyclics are Direct Sums of Projective and CS or Noetherian

R is called a right WV -ring if each simple right R-module is injective relative to proper cyclics. If R is a right WV -ring, then R is right uniform or a right V -ring. It is shown that for a right WV-ring R, R is right noetherian if and only if each right cyclic module is a direct sum of a projective module and a CS or noetherian module. For a finitely generated module M with projective socle over a V -ring R such that every subfactor of M is a direct sum of a projective module and a CS or noetherian module, we show M = X \oplus T, where X is semisimple and T is noetherian with zero socle. In the case that M = R, we get R = S \oplus T, where S is a semisimple artinian ring, and T is a direct sum of right noetherian simple rings with zero socle. In addition, if R is a von Neumann regular ring, then it is semisimple artinian.Comment: A Para\^itre Glasgow Mathematical Journa

Lithium and Gallium Vacancies in LiGaO\u3csub\u3e2\u3c/sub\u3e Crystals

Lithium gallate (LiGaO2) is a wide-band-gap semiconductor with an optical gap greater than 5.3 eV. When alloyed with ZnO, this material offers broad functionality for optical devices that generate, detect, and process light across much of the ultraviolet spectral region. In the present paper, electron paramagnetic resonance (EPR) is used to identify and characterize neutral lithium vacancies (V0Li) and doubly ionized gallium vacancies (V2−Ga) in LiGaO2 crystals. These S = 1/2 native defects are examples of acceptor-bound small polarons, where the unpaired spin (i.e., the hole) is localized on one oxygen ion adjacent to the vacancy. Singly ionized lithium vacancies (V−Li) are present in as-grown crystals and are converted to their paramagnetic state by above-band-gap photons (x rays are used in this study). Because there are very few gallium vacancies in as-grown crystals, a post-growth irradiation with high-energy electrons is used to produce the doubly ionized gallium vacancies (V2−Ga). The EPR spectra allow us to establish detailed models for the two paramagnetic vacancies. Anisotropy in their g matrices is used to identify which of the oxygen ions adjacent to the vacancy has trapped the hole. Both spectra also have resolved structure due to hyperfine interactions with 69Ga and 71Ga nuclei. The V0Li acceptor has nearly equal interactions with Ga nuclei at two Ga sites adjacent to the trapped hole, whereas the V2−Ga acceptor has an interaction with Ga nuclei at only one adjacent Ga site

Copper Doping of ZnO Crystals by Transmutation of \u3csup\u3e64\u3c/sup\u3eZn to \u3csup\u3e65\u3c/sup\u3eCu: An Electron Paramagnetic Resonance and Gamma Spectroscopy Study

Transmutation of 64Zn to 65Cu has been observed in a ZnO crystal irradiated with neutrons. The crystal was characterized with electron paramagnetic resonance (EPR) before and after the irradiation and with gamma spectroscopy after the irradiation. Major features in the gamma spectrum of the neutron-irradiated crystal included the primary 1115.5 keV gamma ray from the 65Zn decay and the positron annihilation peak at 511 keV. Their presence confirmed the successful transmutation of 64Zn nuclei to 65Cu. Additional direct evidence for transmutation was obtained from the EPR of Cu2+ ions (where 63Cu and 65Cu hyperfine lines are easily resolved). A spectrum from isolated Cu2+ (3d9) ions acquired after the neutron irradiation showed only hyperfine lines from 65Cu nuclei. The absence of 63Cu lines in this Cu2+ spectrum left no doubt that the observed 65Cu signals were due to transmuted 65Cu nuclei created as a result of the neutron irradiation. Small concentrations of copper, in the form of Cu+-H complexes, were inadvertently present in our as-grown ZnO crystal. These Cu+-H complexes are not affected by the neutron irradiation, but they dissociate when a crystal is heated to 900 °C. This behavior allowed EPR to distinguish between the copper initially in the crystal and the copper subsequently produced by the neutron irradiation. In addition to transmutation, a second major effect of the neutron irradiation was the formation of zinc and oxygen vacancies by displacement. These vacancies were observed with EPR

Oxygen Vacancies in LiAlO\u3csub\u3e2\u3c/sub\u3e Crystals

Singly ionized oxygen vacancies are produced in LiAlO2 crystals by direct displacement events during a neutron irradiation. These vacancies, with one trapped electron, are referred to as V+O centers. They are identified and characterized using electron paramagnetic resonance (EPR) and optical absorption. The EPR spectrum from the V+O centers is best monitored near 100 K with low microwave power. When the magnetic field is along the [001] direction, this spectrum has a g value of 2.0030 and well-resolved hyperfine interactions of 310 and 240 MHz with the two 27Al nuclei that are adjacent to the oxygen vacancy. A second EPR spectrum, also showing hyperfine interactions with two 27Al nuclei, is attributed to a metastable state of the V+O center. An optical absorption band peaking near 238 nm is assigned to V+O centers. Bleaching light from a Hg lamp converts a portion of the V+O centers to V0O centers (these latter centers are oxygen vacancies with two trapped electrons). The V0O centers have an absorption band peaking near 272 nm, a photoluminescence band peaking near 416 nm, and a photoluminescence excitation band peaking near 277 nm. Besides the oxygen-vacancy EPR spectra, a holelike spectrum with a resolved, but smaller, hyperfine interaction with one 27Al nucleus is present in LiAlO2 after the neutron irradiation. This spectrum is tentatively assigned to doubly ionized aluminum vacancies

Identification of the Zinc-oxygen Divacancy in ZnO Crystals

An electron paramagnetic resonance (EPR) spectrum in neutron-irradiated ZnO crystals is assigned to the zinc-oxygen divacancy. These divacancies are observed in the bulk of both hydrothermally grown and seeded-chemical-vapor-transport-grown crystals after irradiations with fast neutrons. Neutral nonparamagnetic complexes consisting of adjacent zinc and oxygen vacancies are formed during the irradiation. Subsequent illumination below ∼150 K with 442 nm laser light converts these (V2−Zn − V2+O)0 defects to their EPR-active state (V−Zn − V2+O)+ as electrons are transferred to donors. The resulting photoinduced S = 1/2 spectrum of the divacancy is holelike and has a well-resolved angular dependence from which a complete g matrix is obtained. Principal values of the g matrix are 2.00796, 2.00480, and 2.00244. The unpaired spin resides primarily on one of the three remaining oxygen ions immediately adjacent to the zinc vacancy, thus making the electronic structure of the (V−Zn − V2+O)+ ground state similar to the isolated singly ionized axial zinc vacancy. The neutral (V2−Zn − V2+O)0 divacancies dissociate when the ZnO crystals are heated above 250 °C. After heating above this temperature, the divacancy EPR signal cannot be regenerated at low temperature with light

Justice at Sea: Fishers’ politics and marine conservation in coastal Odisha, India

This is a paper about the politics of fishing rights in and around the Gahirmatha marine sanctuary in coastal Odisha, in eastern India. Claims to the resources of this sanctuary are politicised through the creation of a particularly damaging narrative by influential Odiya environmental actors about Bengalis, as illegal immigrants who have hurt the ecosystem through their fishing practices. Anchored within a theoretical framework of justice as recognition, the paper considers the making of a regional Odiya environmentalism that is, potentially, deeply exclusionary. It details how an argument about ‘illegal Bengalis’ depriving ‘indigenous Odiyas’ of their legitimate ‘traditional fishing rights’ derives from particular notions of indigeneity and territory. But the paper also shows that such environmentalism is tenuous, and fits uneasily with the everyday social landscape of fishing in coastal Odisha. It concludes that a wider class conflict between small fishers and the state over a sanctuary sets the context in which questions about legitimate resource rights are raised, sometimes with important effects, like when out at sea

On handling urban informality in southern Africa

In this article I reconsider the handling of urban informality by urban planning and management systems in southern Africa. I argue that authorities have a fetish about formality and that this is fuelled by an obsession with urban modernity. I stress that the desired city, largely inspired by Western notions of modernity, has not been and cannot be realized. Using illustrative cases of top–down interventions, I highlight and interrogate three strategies that authorities have deployed to handle informality in an effort to create or defend the modern city. I suggest that the fetish is built upon a desire for an urban modernity based on a concept of formal order that the authorities believe cannot coexist with the “disorder” and spatial “unruliness” of informality. I question the authorities' conviction that informality is an abomination that needs to be “converted”, dislocated or annihilated. I conclude that the very configuration of urban governance and socio-economic systems in the region, like the rest of sub-Saharan Africa, renders informality inevitable and its eradication impossible