共查询到20条相似文献,搜索用时 31 毫秒
1.
Huan Yin CHEN 《数学学报(英文版)》2007,23(2):357-364
Let R be an exchange ring with primitive factors artinian. We prove that there exists a u∈U(R) such that 1R ± u ∈ U(R), if and only if for any a ∈ R, there exists a u ∈ U(R) such that a ± u∈ U(R). Phrthermore, we prove that, for any A ∈ Mn(R)(n ≥ 2), there exists a U ∈ GLn(R) such that A ± U ∈ GLn(R). 相似文献
2.
Huanyin CHEN 《数学年刊B辑(英文版)》2009,30(3):221-230
The necessary and sufficient conditions under which a ring satisfies regular power-substitution are investigated. It is shown that a ring R satisfies regular powersubstitution if and only if a-b in R implies that there exist n ∈ N and a U E GLn (R) such that aU = Ub if and only if for any regular x ∈ R there exist m,n ∈ N and U ∈ GLn(R) such that x^mIn = xmUx^m, where a-b means that there exists x,y, z∈ R such that a =ybx, b = xaz and x= xyx = xzx. It is proved that every directly finite simple ring satisfies regular power-substitution. Some applications for stably free R-modules are also obtained. 相似文献
3.
Vincenzo De Filippis 《Proceedings Mathematical Sciences》2010,120(3):285-297
Let R be a prime ring, U the Utumi quotient ring of R, C = Z(U) the extended centroid of R, L a non-central Lie ideal of R, H and G non-zero generalized derivations of R. Suppose that there exists an integer n ≥ 1 such that (H(u)u − uG(u))
n
= 0, for all u ∈ L, then one of the following holds: (1) there exists c ∈ U such that H(x) = xc, G(x) = cx; (2) R satisfies the standard identity s
4 and char (R) = 2; (3) R satisfies s
4 and there exist a, b, c ∈ U, such that H(x) = ax+xc, G(x) = cx+xb and (a − b)
n
= 0. 相似文献
4.
Huanyin Chen 《Czechoslovak Mathematical Journal》2006,56(1):9-18
In this paper, we introduce related comparability for exchange ideals. Let I be an exchange ideal of a ring R. If I satisfies related comparability, then for any regular matrix A ∈ M
n
(I), there exist left invertible U
1; U
2 ∈ M
n
(R) and right invertible V
1, V
2 ∈ M
n
(R) such that U
1
V
1
AU
2
V
2 = diag(e
1,..., e
n
) for idempotents e
1,..., e
n
∈ I. 相似文献
5.
《代数通讯》2013,41(6):2771-2789
Abstract A ring R is called strongly stable if whenever aR + bR = R, there exists a w ∈ Q(R) such that a + bw ∈ U(R), where Q(R) = {x ∈ R ∣ ? e ? e 2 ∈ J(R), u ∈ U(R) such that x = eu}. These rings are shown to be a natural generalization of semilocal rings and unit regular rings. We investigate the extensions of strongly stable rings. K 1-groups of such rings are also studied. In this way we recover and extend some results of Menal and Moncasi. 相似文献
6.
7.
Huanyin Chen 《代数通讯》2013,41(8):3913-3924
In this paper, we show that a ring R satisfies unit 1-stable range if and only if a1R + ? + amR = dR with m ≥ 2,a 1, ?am ?R implies that there exist u1 , ?um ? U(R) such that a1u1 +?+amum = d and an exchange ring R has stable range one if and only if a1R+?+amR = dR with m ≥ 2,a 1,?,am ? R implies that there exist unit-regular w 1,?,wm ? R such that a1w1 +?+ amwm = d. Also we show that an exchange ring R satisfies the n-stable range condition if and only if a( nR)+bR = dR with a ? Rn,b,d ? R implies that there exist unimodular regular w ? n R and: y ? R such that aw+by = d. 相似文献
8.
BASUDEB DHARA 《Proceedings Mathematical Sciences》2012,122(1):121-128
Let R be a prime ring with its Utumi ring of quotient U, H and G be two generalized derivations of R and L a noncentral Lie ideal of R. Suppose that there exists 0 ≠ a ∈ R such that a(H(u)u − uG(u))
n
= 0 for all u ∈ L, where n ≥ 1 is a fixed integer. Then there exist b′,c′ ∈ U such that H(x) = b′x + xc′, G(x) = c′x for all x ∈ R with ab′ = 0, unless R satisfies s
4, the standard identity in four variables. 相似文献
9.
Huanyin Chen 《Czechoslovak Mathematical Journal》2008,58(2):417-428
An exchange ring R is strongly separative provided that for all finitely generated projective right R-modules A and B, A ⊕ A ≅ A ⊕ B ⇒ A ≅ B. We prove that an exchange ring R is strongly separative if and only if for any corner S of R, aS + bS = S implies that there exist u, v ∈ S such that au = bv and Su + Sv = S if and only if for any corner S of R, aS + bS = S implies that there exists a right invertible matrix ∈ M
2(S). The dual assertions are also proved. 相似文献
10.
A principal right ideal of a ring is called uniquely generated if any two elements of the ring that generate the same principal right ideal must be right associated (i.e., if for all a,b in a ring R, aR = bR implies a = bu for some unit u of R). In the present paper, we study “uniquely generated modules” as a module theoretic version of “uniquely generated ideals,” and we obtain a characterization of a unit-regular endomorphism ring of a module in terms of certain uniquely generated submodules of the module among some other results: End(M) is unit-regular if and only if End(M) is regular and all M-cyclic submodules of a right R-module M are uniquely generated. We also consider the questions of when an arbitrary element of a ring is associated to an element with a certain property. For example, we consider this question for the ring R[x;σ]∕(xn+1), where R is a strongly regular ring with an endomorphism σ be an endomorphism of R. 相似文献
11.
A. A. Tuganbaev 《Journal of Mathematical Sciences》2009,162(5):730-739
For any ring A, there exist a Bezout ring R and an idempotent e ∈ R with A ≅ eRe. Every module over any ring is a direct summand of an endo-Bezout module. Over any ring, every free module of infinite rank
is an endo-Bezout module. 相似文献
12.
A k-edge-weighting w of a graph G is an assignment of an integer weight, w(e) ∈ {1,…,k}, to each edge e. An edge-weighting naturally induces a vertex coloring c by defining c(u) = Σ
e∋u
w(e) for every u ∈ V (G). A k-edge-weighting of a graph G is vertex-coloring if the induced coloring c is proper, i.e., c(u) ≠ c(v) for any edge uv ∈ E(G). When k ≡ 2 (mod 4) and k ⩾ 6, we prove that if G is k-colorable and 2-connected, δ(G) ⩾ k − 1, then G admits a vertex-coloring k-edge-weighting. We also obtain several sufficient conditions for graphs to be vertex-coloring k-edge-weighting.
相似文献
13.
Ioan I. Vrabie 《Israel Journal of Mathematics》1979,32(2-3):221-235
LetX be a real Banach space,U ⊂X a given open set,A ⊂X×X am-dissipative set andF:C(0,a;U) →L
∞(0,a;X) a continuous mapping. Assume thatA generates a nonlinear semigroup of contractionsS(t): {ie221-2}) → {ie221-3}), strongly continuous at the origin, withS(t) compact for allt>0. Then, for eachu
0 ∈ {ie221-4}) ∩U there existsT ∈ ]0,a] such that the following initial value problem: (du(t))/(dt) ∈Au(t) +F(u)(t),u(0)=u
0, has at least one integral solution on [0,T]. Some extensions and applications are also included. 相似文献
14.
Juan Luis Vázquez 《Israel Journal of Mathematics》1982,43(3):255-272
The semilinear perturbation of Poisson’s equation (E): −Δu+β(u)∋f, where β is a maximal monotone graph inR, has been investigated by Ph. Bénilan, H. Brézis and M. Crandall forf∈L
1(R
N
),N≧1, under the assumptions 0∈β(0) ifN≧3 and 0∈β(0) ∩ Int β(R) ifN=1,2. We discuss in this paper the solvability and well-posedness of (E) in terms of any maximal monotone graph β. In particular,
if β takes only positive values andN≧3 we prove that no solution exists; ifN=2 we give necessary and sufficient conditions on β andf for (E) to be solvable in a natural sense. 相似文献
15.
Huanyin Chen 《数学年刊B辑(英文版)》2007,28(6):617-628
A ring R is a QB-ring provided that aR + bR = R with a, b ∈ R implies that there exists a y ∈ R such that
It is said that a ring R is a JB-ring provided that R/J(R) is a QB-ring, where J(R) is the Jacobson radical of R. In this paper, various necessary and sufficient conditions, under which a ring is a JB-ring, are established. It is proved that JB-rings can be characterized by pseudo-similarity. Furthermore, the author proves that R is a JB-ring iff so is R/J(R)2. 相似文献
16.
Let R be a prime ring of char R ≠ 2 with a nonzero derivation d and let U be its noncentral Lie ideal. If for some fixed integers n
1 ⩾ 0, n
2 ⩾ 0, n
3 ⩾ 0, (u
n1 [d(u), u]u
n2)
n3 ∈ Z(R) for all u ∈ U, then R satisfies S
4, the standard identity in four variables. 相似文献
17.
FangGui Wang 《中国科学A辑(英文版)》2009,52(1):94-108
Let (R,m) be a local GCD domain. R is called a U2 ring if there is an element u ∈ m-m2 such that R/(u) is a valuation domain and Ru is a B′ezout domain. In this case u is called a normal element of R. In this paper we prove that if R is a U2 ring, then R and R[x] are coherent; moreover, if R has a normal element u and dim(R/(u)) = 1, then every finitely generated projective module over R[X] is free. 相似文献
18.
A semiring S whose additive reduct is a semilattice is called a k-regular semiring if for every a∈S there is x∈S such that a+axa=axa. For a semigroup F, the power semiring P(F) is a k-regular semiring if and only if F is a regular semigroup. An element e∈S is a k-idempotent if e+e
2=e
2. Basic properties of k-regular semirings whose k-idempotents are commutative have been studied. 相似文献
19.
Huanyin Chen 《代数通讯》2013,41(5):1661-1673
A regular ring R is separative provided that for all finitely generated projective right R-modules A and B, A⊕ A? A⊕ B? A⊕ B implies that A? B. We prove, in this article, that a regular ring R in which 2 is invertible is separative if and only if each a ∈ R satisfying R(1 ? a 2)R = Rr(a) = ?(a)R and i(End R (aR)) = ∞ is unit-regular if and only if each a ∈ R satisfying R(1 ? a 2)R ∩ RaR = Rr(a) ∩ ?(a)R ∩ RaR and i(End R (aR)) = ∞ is unit-regular. Further equivalent characterizations of such regular rings are also obtained. 相似文献
20.