Let R be a prime ring, I a nonzero ideal of R and n a fixed positive integer. If R admits a generalized derivation F associated with a derivation d such that c for all x, $y{\in}I$. Then either R is ...commutative or n = 1, d = 0 and F is the identity map on R. Moreover in case R is a semiprime ring and $(F(x,\;y))^n=x,\;y$ for all x, $y{\in}R$, then either R is commutative or n = 1, $d(R){\subseteq}Z(R)$, R contains a non-zero central ideal and for all $x{\in}R$.
Let R be a prime ring, I a nonzero ideal of R and n a fixed positive integer.
If R admits a generalized derivation F associated with a derivation d such that (F(x,y))^n=x,y for all x, y∈ I. Then ...either R is commutative or n=1, d=0 and F is the identity map on R. Moreover in case R is a semiprime ring and (F(x,y))^n=x, y for all x, y∈ R, then either R is commutative or n=1, d(R)⊆ Z(R), R contains a non-zero central ideal and F(x)-x ∈ Z(R) for all x∈ R. KCI Citation Count: 5
Let
R
be a prime ring of characteristic different from 2,
U
its Utumi quotient ring,
C
the center of
U
,
F
a non-zero generalized derivation of
R
and
L
a non-commutative Lie ideal of
R
. Suppose that ...there exists
0
≠
a
∈
R
such that
a
(
u
s
F
(
u
)
,
u
u
t
)
n
=
0
for all
u
∈
L
, where
s
≥
0
,
t
≥
0
,
n
≥
1
are fixed integers. Then either
F
(
x
)
=
α
x
for all
x
∈
R
with
α
∈
C
or
R
satisfies
s
4
(
x
1
,
…
,
x
4
)
, the standard identity in four variables, and
F
(
x
)
=
b
x
+
x
b
+
α
x
for all
x
∈
R
, for some
b
∈
U
and
α
∈
C
.
Let R be a prime ring, I a nonzero ideal of R, and a ∈ R. Suppose that σ is a nontrivial automorphism of R such that a{(σ(x ∘ y))n − (x ∘ y)m} = 0 or a{(σ(x,y))n − (x,y)m} = 0 for all x,y ∈ I, where ...n and m are fixed positive integers. We prove that if char(R) > n + 1 or char(R) = 0, then either a = 0 or R is commutative.
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
Let \(\mathscr{R}\) be a prime ring of Char\((\mathscr{R}) \neq 2\) and \(m\neq 1\) be a positive integer. If \(S\) is a nonzero skew derivation with an associated automorphism \(\mathscr{T}\) of ...\(\mathscr{R}\) such that \((S(a, b), a, b)^{m} = S(a, b), a, b\) for all \(a, b \in \mathscr{R}\), then \(\mathscr{R}\) is commutative.
Let (
R
, *) be a 2-torsion free *-prime ring with involution *,
L
≠ 0 be a square closed *-Lie ideal of
R
and
α, β
automorphisms of
R
commuting with *. An additive mapping
F
:
R
→
R
is called a ...generalized (
α, β
)-derivation on
R
if there exists an (
α, β
)-derivation
d
such that
F
(
xy
) =
F
(
x
)
α
(
y
) +
β
(
x
)
d
(
y
) holds for all
. In the present paper, we shall show that
such that
R
is a *-prime ring admits a generalized (
α, β
)-derivation satisfying several conditions, but associated with an (
α, β
)-derivation commuting with *.
OBJECTIVE：To evaluate the effectiveness of a combined Traditional Chinese Medicine（TCM） therapy versus conventional treatment on adolescent idiopathic scoliosis.METHODS：One hundred twenty outpatients ...with mild and moderate adolescent idiopathic scoliosis were randomly divided into a TCM group（TCMG）and a brace group（CG）.TCMG patients underwent Daoyin,Tuina,and acupotomology therapies.CG patients were treated with a Milwaukee brace.Each patient＇s Cobb angle was measured after 12 and 24 months of treatment,and pulmonary function was determined after 12 months of treatment.Average electromyogram（AEMG） ratio of the surface electromyogram was measured after 6 and 12 months of treatment and followed-up after 18 and 24 months.RESULTS：The Cobb angle significantly decreased in both groups after 12 months of treatment compared with before treatment（P〈 0.05）.The percentages of original Cobb angle in TCMG and CG were51.4%and 47.8%（P 〉 0.05） after 12 months and62.5%and 34.7%（P 〈 0.05） after 24 months,respectively.Pulmonary function significantly improved after 12 months in TCMG（P 〈 0.05） but significantly decreased in CG（P 〈 0.05）.The AEMG ratio was significantly lower（P 〈 0.01） and tended to remain at1 after stopping treatment in TCMG,but increased in CG（P〈0.05）.CONCLUSION：TCM combined therapy can prevent the progression of scoliosis.The AEMG ratio is a promising index that could replace radiography in the evaluation of treatment effect and progression in scoliosis.
Iron oxide is a promising anode material for lithium ion batteries, but it usually exhibits poor electrochemical property because of its poor conductivity and large volume variation during the ...lithium uptake and release processes. In this work, a double protection strategy for improving electrochemical performance of Fe3O4 nanoparticles through the use of decoration with multi-walled carbon nanotubes and reduced graphene oxides networks has been developed. The resulting MWCNTs-Fe3O4-rGO nanocomposites exhibited excellent cycling performance and rate capability in comparison with MWCNTs-Fe3O4, MWCNTs-Fe3O4 physically mixed with rGO, and Fe3O4-rGO. A reversible capacity of -680 mA·h·g^-1 can be maintained after 100 cycles under a current density of 200 mA.g^-1.
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