The classes of FP -injective and weakly quasi-Frobenius rings are investigated. The properties for both classes of rings are closely linked with embedding of finitely presented modules in fp-flat and free modules respectively. Using these properties, we characterize the classes of coherent CF and FGF-rings. Moreover, it is proved that the group ring R(G) is FP -injective (weakly quasi-Frobenius...

an octahedral cobalt(iii) complex, trans-[(me2bpb)co(bzlan)2]clo4 (1), with h2me2bpb = n,n’-(4,5-dimethyl-1,2-phenylene)dipicolinamide and bzlan = benzylamine, has been synthesized and characterized by elemental analyses, ir, uv-vis, and 1h nmr spectroscopy. the structure of this complex has been determined by x-ray crystallography. the me2bpb2– is a di-anionic tetradentate ligand furnishing a ...

We propose to generate steady-state microbunching in a storage ring with a reversible seeding scheme. High gain harmonic generation (HGHG) and echo-enabled harmonic generation (EEHG) are two promising methods for microbunching linac electron beams. Because both schemes increase the energy spread of the seeded beam, they cannot drive a coherent radiator turn-by-turn in a storage ring. However, r...

in this paper, we introduce a new generalization of weakly prime ideals called $i$-prime. suppose $r$ is a commutative ring with identity and $i$ a fixed ideal of $r$. a proper ideal $p$ of $r$ is $i$-prime if for $a, b in r$ with $ab in p-ip$ implies either $a in p$ or $b in p$. we give some characterizations of $i$-prime ideals and study some of its properties.  moreover, we give conditions  ...