let r be an associative ring with unity. an element a in r is said to be r-clean if a = e+r, where e is an idempotent and r is a regular (von neumann) element in r. if every element of r is r-clean, then r is called an r-clean ring. in this paper, we prove that the concepts of clean ring and r-clean ring are equivalent for abelian rings. further we prove that if 0 and 1 are the only idempotents...

let r be an associative ring with unity. an element a in r is said to be r-clean if a = e+r, where e is an idempotent and r is a regular (von neumann) element in r. if every element of r is r-clean, then r is called an r-clean ring. in this paper, we prove that the concepts of clean ring and r-clean ring are equivalent for abelian rings. further we prove that if 0 and 1 are the only idempotents...

Ring diagram analysis of solar oscillation power spectra obtained from MDI data is carried out to study the velocity fields in the outer part of the solar convection zone. The three dimensional power spectra are fitted to a model which has a Lorentzian profile in frequency and which includes the advection of the wave front by horizontal flows, to obtain the two components of the sub-surface flo...

Let N be a near-ring. In this paper, we associate a graph corresponding to the 3-prime radical I of N , denoted by ΓI(N). Further we obtain certain topological properties of Spec(N), the spectrum of 3-prime ideals of N and graph theoretic properties of ΓI(N). Using these properties, we discuss dominating sets and connected dominating sets of ΓI(N).

U. Hechtfischer,1 Z. Amitay,2 P. Forck,1 M. Lange,1 J. Linkemann,1 M. Schmitt,1 U. Schramm,1 D. Schwalm,1 R. Wester,1 D. Zajfman,2 and A. Wolf1 1Max-Planck-Institut für Kernphysik und Physikalisches Institut der Universität Heidelberg, 69029 Heidelberg, Germany 2Department of Particle Physics, Weizmann Institute of Science, Rehovot, 76100, Israel (Received 12 November 1997) Photodissociation of...

Radiation belts of MeV protons have been observed just outward of Saturn's main rings. During the final stages of the mission, the Cassini spacecraft will pass through the gap between the main rings and the planet. Based on how the known radiation belts of Saturn are formed, it is expected that MeV protons will be present in this gap and also bounce through the tenuous D ring right outside the ...

S. D. Scott has shown that the group of automorphisms of the near ring generated by the automorphisms of a given group is isomorphic to the automorphism group of the given group if that group's automorphism is complete. Here that theorem is generalized by showing that the group of automorphisms of a near ring distributively generated by its units is a subgroup of the group of automorphisms of t...

We give a survey of our use of computers in near-ring theory.

We have demonstrated efficient amplification of near-infrared, 0.83-μm and 1.06-μm light, in a photorefractive ring resonator using Rh:BaTiO3. The optical power oscillating inside the ring exceeded the pump power by a factor of up to 2.34. The sensitivity of a ring resonator to nanometer changes in its length was characterised using a piezo-mirror. PACS: 42.65. Hw; 42.70.Nq; 42.60.Da Photorefra...