Let R be a ring. R is called right AP-injective if, for any a ∈ R, there exists a left ideal of R such that lr(a) = Ra (?) Xa. We extend this notion to modules. A right .R-module M with 5 = End(MR) is called quasi AP-injective if, for any s ∈ S, there exists a left ideal Xs of S such that ls(Ker(s)) = Ss (?) Xs. In this paper, we give some characterizations and properties of quasi AP-injective modules which generalize results of Page and Zhou. 相似文献
A dense-phase latex rubber tube and a polyporous propylene hollow-fiber membrane module (HFMM) were investigated for control
of benzene-contaminated gas streams. The abiotic mass flux observed through the latex tube was 3.9–13 mg/(min·m2) for 150 ppm of benzene at various gas and liquid flow rates, while a 100-fold lower mass flux was observed in the HFMM.
After seeding with an aromatic-degrading culture enriched from activated sludge, the observed removal was 80% of 150 ppm,
corresponding toa mass flux of 45 mg/(min·m2). The observed mass flux through the HFMM during biofiltration also rose, to 0.4 mg/(min·m2). Because the HFMM had a 50-fold higher surface area than the latex tube, the observed ben zene removal was 99.8%. Compared
to conventional biofilters, the two reactors had modest elimination capacities, 2.5–18 g/(m3·h) in the latex tube membrane bioreactor and 4.8–58 g/(m3·h) in the HFMM. Although the HFMM had a higher elimination capacity, the gas-phase pressure drop was much greater. 相似文献
Tensor products of Calgebras over an abelian Walgebra are studied. The minimal Cnorm on is shown to be just the quotient of the minimal Cnorm on if or is exact.
Let be an algebraically closed field containing which is complete with respect to an absolute value . We prove that under suitable constraints on the coefficients, the series converges to a surjective, open, continuous -linear homomorphism whose kernel is locally compact. We characterize the locally compact sub--vector spaces of which occur as kernels of such series, and describe the extent to which determines the series. We develop a theory of Newton polygons for these series which lets us compute the Haar measure of the set of zeros of of a given valuation, given the valuations of the coefficients. The ``adjoint' series converges everywhere if and only if does, and in this case there is a natural bilinear pairing
which exhibits as the Pontryagin dual of . Many of these results extend to non-linear fractional power series. We apply these results to construct a Drinfeld module analogue of the Weil pairing, and to describe the topological module structure of the kernel of the adjoint exponential of a Drinfeld module.
A (right -) module is said to be a Whitehead test module for projectivity (shortly: a p-test module) provided for each module , implies is projective. Dually, i-test modules are defined. For example, is a p-test abelian group iff each Whitehead group is free. Our first main result says that if is a right hereditary non-right perfect ring, then the existence of p-test modules is independent of ZFC + GCH. On the other hand, for any ring , there is a proper class of i-test modules. Dually, there is a proper class of p-test modules over any right perfect ring.
A non-semisimple ring is said to be fully saturated (-saturated) provided that all non-projective (-generated non-projective) modules are i-test. We show that classification of saturated rings can be reduced to the indecomposable ones. Indecomposable 1-saturated rings fall into two classes: type I, where all simple modules are isomorphic, and type II, the others. Our second main result gives a complete characterization of rings of type II as certain generalized upper triangular matrix rings, . The four parameters involved here are skew-fields and , and natural numbers . For rings of type I, we have several partial results: e.g. using a generalization of Bongartz Lemma, we show that it is consistent that each fully saturated ring of type I is a full matrix ring over a local quasi-Frobenius ring. In several recent papers, our results have been applied to Tilting Theory and to the Theory of -modules.
In this work it is reported that the kinetic modelling of the separation of cadmium from phosphoric acid by non-dispersive solvent extraction. Using Cyanex 302 as selective extractant, the extraction step was carried out in a hollow fibre module containing polypropylene fibres, whereas the concentration step required a ceramic module with tubular channels due to the high acidity of the backextraction agent. Application of the methodology previously reported by the authors led to the development of a kinetic model with three design parameters, i.e., equilibrium constant of the extraction reaction (K'e = 6 × 103 mol−2/l−2), membrane mass transport coefficient of the extraction module Kme=8.33×10−8 m/s) and of the backextraction module (Kms=3.33×10−8 m/s), that described satisfactorily the behaviour of the separation-concentration system. Thus, in this work a new application of the non-dispersive solvent extraction technology is presented, characterising at the same time the behaviour and parameters of a new type of contactor, i.e., a tubular ceramic module. 相似文献
The concept of crystalline module, that is, an unambiguously isolated, repeated quasi-molecular element, is introduced. This concept is more general than the concept of crystal lattice. The generalized modular approach allows extension of the methods and principles of crystallography to quasi-crystals, clusters, amorphous solids, and periodic biological structures. Principles of construction of aperiodic, nonequilibrium regular modular structures are formulated. Limitations on the size of icosahedral clusters are due to the presence of spherical shells with non-Euclidean tetrahedral tiling in their structure. A parametric relationship between the structures of icosahedral fullerenes and metal clusters of the Chini series was found. 相似文献