Let $D$ be a division ring with center $F$, and $G$ subnormal or quasinormal subgroup of $D^*$. We show that if is locally solvable, then contained in $F$.

The current paper studied the concept of right n-derivation satisfying certified conditions on semigroup ideals near-rings and some related properties. Interesting results have been reached, most prominent which are following: Let M be a 3-prime left near-ring A_1,A_2,…,A_n nonzero M, if d is satisfies following conditions,d(u_1,u_2,…,(u_j,v_j ),…,u_n )=0 ∀ 〖 u〗_1 〖ϵA〗_1 ,u_2 〖ϵA〗_2,…,u_j,v_j ϵ...

for a ring endomorphism $alpha$ and an $alpha$-derivation $delta$, we introduce a concept, so called skew $pi$-armendariz ring, that is a generalization of both $pi$-armendariz rings, and $(alpha,delta)$-compatible skew armendariz rings. we first observe the basic properties of skew $pi$-armendariz rings, and extend the class of skew $pi$-armendariz rings through various ring extensions. we nex...

The origin of the methyl group on carbon atom 1 of Ring A of the corrin ring of vitamin Blz was investigated by W and lH magnetic resonance spectroscopy. Recently we found by the same technique that this methyl group does not originate from the S-carbon atom of d-aminolevulinic acid. This was of considerable interest, for it has been considered that in the fusion of Rings A and D the potential ...

Previous investigations of Saturn’s outer D ring (73,200–74,000 km from Saturn’s center) identified periodic brightness variations whose radial wavenumber increased linearly over time. This pattern was attributed to a vertical corrugation, and its temporal variability implied that some event – possibly an impact with interplanetary debris – caused the ring to become tilted out the planet’s equa...

A convergent total synthesis of ouabagenin, an aglycon of cardenolide glycoside ouabain, was achieved by assembly of the AB-ring, D-ring and butenolide moieties. The multiply oxygenated cis-decalin structure of the AB-ring was constructed from (R)-perillaldehyde through the Diels-Alder reaction and sequential oxidations. The intermolecular acetal formation of the AB-ring and D-ring fragments, a...

A convergent total synthesis of ouabagenin, an aglycon of cardenolide glycoside ouabain, was achieved by assembly of the AB-ring, D-ring and butenolide moieties. The multiply oxygenated cis-decalin structure of the AB-ring was constructed from (R)-perillaldehyde through the Diels–Alder reaction and sequential oxidations. The intermolecular acetal formation of the AB-ring and D-ring fragments, a...

four known flavonoids: quercetin 3-o-β-d-rutinoside (q3rut), myricetin 3-o-β-d-galactopyranoside (m3gal), quercetin 3-o-β-d-galactopyranoside (q3gal) and quercetin 3-o-β-d-glucopyranoside (q3glc), for the first time were isolated from aerial parts of euphorbia microsciadia. the chemical structure of them was elucidated on the basis of 1 and 2 d-nmr spectra and different spectroscopic techniques...

in this paper, we introduce the new notion of n-f-clean rings as a generalization of f-clean rings. next, we investigate some properties of such rings. we prove that mn(r) is n-f-clean for any n-f-clean ring r. we also, get a condition under which the denitions of n-cleanness and n-f-cleanness are equivalent.