On Jordan and Jordan*-Generalized Derivations in Semiprime Rings with Involution
The purpose of this note is to prove the following result. Let R be a6 −torsion free semiprime *-ring and let G: R−→R be an additive mapping such that G(xyx )= G(x)y ∗ x ∗ + xD(y)x ∗ + xyD(x) holds for all x,y ∈ R and some *-derivations D of R. Then G is a Jordan*generalized derivation.
On some additive mappings in rings with involution
SummaryLetR be a *-ring. We study an additive mappingD: R → R satisfyingD(x2) =D(x)x* +xD(x) for allx ∈ R.It is shown that, in caseR contains the unit element, the element 1/2, and an invertible skew-hermitian element which lies in the center ofR, then there exists ana ∈ R such thatD(x) = ax*− xa for allx ∈ R. IfR is a noncommutative prime real algebra, thenD is linear. In our main result we prove that a noncommutative prime ring of characteristic different from 2 is normal (i.e.xx* =x*x for allx ∈ R) if and only if there exists a nonzero additive mappingD: R → R satisfyingD(x2) =D(x)x* +xD(x) and [D(x), x] = 0 for allx ∈ R. This result is in the spirit of the well-known theorem of E. Posner, which states that the existence of a nonzero derivationD on a prime ringR, such that [D(x), x] lies in the center ofR for allx ∈ R, forcesR to be commutative.
Serum Profiles of Luteinizing Hormone, Oestradiol and Cholesterol and Ovarian Functions in Layer Poultry Birds (Gallus domesticus) Fed Diets Containing Furazolidone
This study was carried out to assess the serum profiles of luteinizing hormone (LH), oestradiol, cholesterol and ovarian functions in layer poultry birds (Rhode Island Red;Gallus domesticus) fed a diet containing various concentrations of furazolidone (FZ). A total of 40 birds were randomly assigned to receive FZ 0, 200, 400 or 800 mg/kg feed (ppm) daily during the pre-laying age, i.e. 13–18 weeks (for 5 weeks). Blood samples were collected at weekly intervals. Concentrations of LH and oestradiol in serum were estimated at alternate weeks using radioimmunoassays. Serum cholesterol levels were analysed by an enzymatic calorimetric method. Furazolidone administration was terminated at the 18th week of age. The birds were sacrificed at 22nd week of age and ovarian tissues were processed for morphometric studies. Serum LH, oestradiol and cholesterol levels were affected by age (p<0.001) and FZ dose (p<0.001). Serum LH and oestradiol levels were lower (p<0.05) in birds receiving FZ 800 mg/kg feed daily compared with the controls, whereas serum cholesterol profiles were lower (p<0.05) in all FZ-administered groups than in the control group. The mean weight of ovaries having no yolky follicles observed in the group receiving FZ 400 or 800 mg/kg feed per day was reduced (p<0.05) compared with the control group. Dosing FZ at 800 mg/kg feed per day reduced (p<0.05) the mean volume of ovaries having no yolky follicles compared with the control group. In birds receiving FZ 800 mg/kg feed per day, the mean length of the oviduct was reduced (p<0.05) as compared with the control group. Morphometric studies revealed that the mean number of oocytes with diameter in the range 401–800 μm decreased (p<0.05) in birds fed FZ 400 or 800 mg/kg feed per day. Initial egg production was affected by age (p<0.001) and dose (p<0.001) of FZ. The mean number of eggs laid by different groups revealed that egg production was reduced (p<0.05) in birds receiving FZ 800 mg/kg feed per day as compared with the controls. The present data suggest that FZ causes suppression in serum profiles of LH, oestradiol, cholesterol and ovarian functions in Rhode Island Red layer poultry birds. Therefore, great care must be taken with use of FZ in layer poultry birds (Gallus domesticus) with regard to dosage and duration of administration.