For any reduced commutative $f$-ring with identity and bounded inversion, we show that a condition which is obviously necessary for the socle of the ring to coincide with the socle of its bounded part, is actually also sufficient. The condition is that every minimal ideal of the ring consist entirely of bounded elements. It is not too stringent, and is satisfied, for instance, by rings of ...

Equatorial/axial conversion in piperidine and phosphorinane with different substituents wereinvestigated with great details. Three possible routes, i.e. heteroatom inversion and two ring inversiontype were considered. Ring conversion can occur via two pathways one starts with ring flatteningfrom the heteroatom site (nitrogen in piperidine and phosphorous in phosphorinane) and the otherinitiates...

to calculation non-bonded interaction of the [cocl6]3- complex embedded in nano ring, we focus on the single wall boron-nitride b18n18 nano ring. thus, the geometry of b18n18 nano ring has been optimized by b3lyp method with epr-ii (electron paramagnetic resonance) basis set and geometry of the [cocl6]3- complex has been optimized at b3lyp method with aldrich’s vtz basis set and stuttgart rsc 1...

In this study, B12N12 Nano ring has been selected because it consist of four 6-side rings and polar bonds B-N which in comparison with non-polar bonds C-C, is more suitable for the study of the absorption of other compounds. So reactivity and stability of Benzene alone and in the presence B12N12 nano ring field checked. To determine the non-bonded interaction energies between Benzene and B12N12...

We prove that the universal unramified deformation ring R of a continuous Galois representation ρ : GF+ → GLn(k) (for a totally real field F and finite field k) is finite over O = W (k) in many cases. We also prove (under similar hypotheses) that the universal deformation ring R is finite over the local deformation ring R.

making capital and investment is the main driving forces of economic development. based on the investment sensitivity to the changes of some of macro-economic variables and risk and uncertainty, the present study evaluated the effective factors on investment in private sector in iran during 1980-2007. at first, the uncertainty variables of real informal exchange rate, nominal interest rate and ...

an r-module m is called epi-retractable if every submodule of mr is a homomorphic image of m. it is shown that if r is a right perfect ring, then every projective slightly compressible module mr is epi-retractable. if r is a noetherian ring, then every epi-retractable right r-module has direct sum of uniform submodules. if endomorphism ring of a module mr is von-neumann regular, then m is semi-...

In this paper, we show that every element of a discrete module is a sum of two units if and only if its endomorphism ring has no factor ring isomorphic to $Z_{2}$. We also characterize unit sum number equal to two for the endomorphism ring of quasi-discrete modules with finite exchange property.

We study central extensions of division rings with orderings of higher level. We show that orderings extend to certain immediate and inert extensions. Further, it is proved that any n–ordered division ring can be extended to a n–ordered division ring with almost real closed center. In the last section an old theorem due to Neumann is generalized: every n–ordered division ring can be extended to...