Orders in regular rings with minimal condition for principal right ideals

ABSTRACT

A ring R is called an n-clean (resp. Σ-clean) ring if every element in R is n-clean (resp. Σ-clean). Clean rings are 1-clean and hence are Σ-clean. An example shows that there exists a 2-clean ring that is not clean. This shows that Σ-clean rings are a proper generalization of clean rings. The group ring ?_(p) G with G a cyclic group of order 3 is proved to be Σ-clean. The m× m matrix ring M _m (R) over an n-clean ring is n-clean, and the m×m (m>1) matrix ring M _m (R) over any ring is Σ-clean. Additionally, rings satisfying a weakly unit 1-stable range were introduced. Rings satisfying weakly unit 1-stable range are left-right symmetric and are generalizations of abelian π-regular rings, abelian clean rings, and rings satisfying unit 1-stable range. A ring R satisfies a weakly unit 1-stable range if and only if whenever a ₁ R + ˙˙˙ a _m R = dR, with m ≥ 2, a ₁,…, a _m, d ∈ R, there exist u ₁ ∈ U(R) and u ₂,…, u _m ∈ W(R) such that a ₁ u ₁ + ? a _m u _m = Rd.     

Diagrammatic structure of the general coupled cluster equations

The general formula for the number of diagrammatic terms occurring in the T_n equation within a particular coupled cluster model is derived. Both the antisymmetrized and Goldstone diagrams are considered. In addition to the full coupled cluster equation approximate approaches are discussed, and for each the general formula for the number of terms is given. Analogous expressions are presented for the number of diagrammatic terms contributing to the elements of the transformed Hamiltonian [Hbar] = e^?T He^T .     

Gadolinium texaphyrin-methotrexate conjugates. Towards improved cancer chemotherapeutic agents

Conjugates between methotrexate (MTX, Matrex, N-[4-[[(2,4-diamino-6-pteridinyl)methyl]methylamino]benzoyl]-l-glutamic acid), an antifolate cancer chemotherapeutic to which resistance is often observed, and motexafin gadolinium (MGd), an experimental agent demonstrating selective tumor localization, are described. These systems were prepared in order to test whether linking these two species would produce agents with enhanced activity relative to MTX alone. Both ester- and amide-linked conjugates were synthesized starting from MGd and MTX. The ester conjugate showed greater in vitro anti-proliferative activity against the A549 lung carcinoma cell line at short incubation times than did MTX alone. Neither the amide conjugate, nor MGd, showed any observable activity under these in vitro conditions. These results are rationalized in terms of enhanced cellular uptake of both the ester and amide conjugates that is coupled with an effective rate of release (e.g., inherent or enzyme-mediated hydrolysis) in the case of the ester-linked conjugate, but not the corresponding amide system.     

Crystal and molecular structure of octacarbonyl[bis(bispentafluorophenylarsenido)] dimolybdenum,Mo2(CO)8[μ-As(C6F5)2]2

The X-ray crystallographic structure determination of Mo₂(CO)₈[-As(C₆F₅)₂]₂ reveals that the compound crystallizes in the tetragonal space groupP42₁ c witha=14.915(3),c=16.732(3) Å,V=3722(1) ų, andZ=4. Least-squares refinement based on 1474 independent observed data [(F _obs)3(F _obs)] resulted in a finalR value of 0.038. The Mo-Mo distance of 3.132(1) Å is longer than found in analogous phosphido-bridged molybdenum systems. The central Mo₂As₂ rhombus is nearly flat and the coordination geometry of the Mo atoms is essentially octahedral. An unusual staggering of the Mo(CO)₄ groups by 15.8° and short intramolecular C₆F₅CO contacts support the presence of a strong steric interaction between the Mo(CO)₄ and As(C₆F₅)₂ groups.     

Fate dynamics of environmentally exposed explosive traces

The chemical and physical fates of trace amounts (<50 μg) of explosives containing 2,4,6-trinitrotoluene (TNT), hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX), and pentaerythritol tetranitrate (PETN) were determined for the purpose of informing the capabilities of tactical trace explosive detection systems. From these measurements, it was found that the mass decreases and the chemical composition changes on a time scale of hours, with the loss mechanism due to a combination of sublimation and photodegradation. The rates for these processes were dependent on the explosive composition, as well as on both the ambient temperature and the size distribution of the explosive particulates. From these results, a persistence model was developed and applied to model the time dependence of both the mass and areal coverage of the fingerprints, resulting in a predictive capability for determining fingerprint fate. Chemical analysis confirmed that sublimation rates for TNT were depressed by UV (330-400 nm) exposure due to photochemically driven increases in the molecular weight, whereas the opposite was observed for RDX. No changes were observed for PETN upon exposure to UV radiation, and this was attributed to its low UV absorbance.     

Recognition of thymine in DNA bulges by a Zn(II) macrocyclic complex

A Zn(II) macrocyclic complex with appended quinoline is a bifunctional recognition agent that uses both the Zn(II) center and the pendent aromatic group to bind to thymine in bulges with good selectivity over DNA containing G, C or A bulges. Spectroscopic studies show that the stem containing the bulge stays largely intact in a DNA hairpin with the Zn(II) complex bound to the thymine bulge.     

Products of idempotent endomorphisms of free acts of infinite rank

In 1966, J. M. Howie characterized the self-maps of a set which can be written as a product (i.e., composite) of idempotent self-maps of that set. Using a wreath product construction introduced by V. Fleischer, the first-named author was recently able to describe products of idempotent endomorphisms of a freeS-act of finite rank whereS is any monoid. The purpose of the present paper is to extend this result to freeS-acts of infinite rank.Research supported by Natural Sciences and Engineering Research Council of Canada Research Grant A4494     

Plane Sources of Waves in the Presence of Magnetic Field

In this paper the generation of harmonic waves in an elastic magneticmaterial, which is a perfect conductor of electricity, isconsidered. It has been assumed that an infinite body is subjected tothe action of an initially constant magnetic fieldH = (H,0,0) and in the plane ax+by=0 acts a source ofdistortion. It has been shown that this source may produce bothtransverse and longitudinal waves and each of them consists of two parts,which propagate with different speeds. The amplitudes and speeds in dependence on theangle between the direction of wave propagation and the magnetic fieldintensity H have been discussed.