共查询到20条相似文献,搜索用时 15 毫秒
1.
A. V. Yakovlev 《Journal of Mathematical Sciences》1997,83(5):680-688
Let Λ be a ring with the following properties: (a) Λ is a direct sum of left ideals P1,..., Pn; (b) every nontrivial homomorphism Pi→Pj is a monomorphism; (c) for every i, j the intersection of any two submodules of Pj isomorphic to Pi contains a submodule isomorphic to Pi. Then Λ can be represented as a subring associated with a net of ideals in a generalized matrix ring. Bibliography: 5 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 211, 1994, pp. 184–198.
Translated by A. V. Yakovlev. 相似文献
2.
Feng WEI 《数学学报(英文版)》2005,21(4):823-832
Let R be a semiprime ring with characteristic p≥0 and RF be its left Martindale quotient ring. If ф(Xi^△j) is a reduced generalized differential identity for an essential ideal of R, then ф(Zije(△j )) is a generalized polynomial identity for RF, where e(△j) are idempotents in the extended centroid of R determined by △j. Let R be a prime ring and Q be its symmetric Martindale quotient ring. If ф(Xi△j) is a reduced generalized differential identity for a noncommutative Lie ideal of R, then ф(Zij) is a generalized polynomial identity for [R, R]. Moreover, if ф(Xi△j) is a reduced generalized differential identity, with coefficients in Q, for a large right ideal of R, then ф(Zij) is a generalized polynomial identity for Q. 相似文献
3.
We construct the Chow ringCH*(X) =CH
0
(X)⊕CH
1
(X)⊕CH
2
(X) of a reduced, quasi-projective surfaceX, together with Chern class mapsc
i
:K
0
(X) → CH
i
(X), with the usual properties. As a consequence, we show that the cycle mapCH
2
(X)→ F
0
K
0
(X) is an isomorphism. Our treatment is greatly influenced by an unpublished 1983 preprint of Levine’s, but is much simpler,
since we deal only with surfaces. 相似文献
4.
Further Results on Finitely Generated Projective Modules 总被引:1,自引:0,他引:1
Tong Suo Wu 《数学学报(英文版)》2002,18(2):225-228
In this paper, the exchange rings R whose primitive factor rings are artinian are studied. The following results are proved: for any exchange ring R and any two-sided ideal I of R, K
0(π) : K
0(R)→K
0(R/I) is a group epimorphism with the kernel {[P]−[Q] |P = PI, Q = QI}; there is an isomorphism of ordered groups from K
0(R) to the gorup of all such functions ƒ
P
: X→Q(P∈p(R)), where X is the set of all primitive ideals of R and Q, the rational integers.
Received February 2, 1999, Accepted December 9, 1999 相似文献
5.
Alexander Nenashev 《K-Theory》2005,34(3):219-232
We interpret the Steinberg symbols xi,j(a) as homotopies contracting the elementary matrices ei,j(a), the latters being represented by certain arcs in a simplicial model of the K-theory. We further prove the Steinberg relations for these homotopies. This provides an explicit map from K2 of a ring, defined classically as ker(St(R) → GL(R)), to π2 of the G-construction assigned to R. Though the two groups are known to be isomorphic, a certain work is to be done to prove that this explicit map is an isomorphism.
Mathematics Subject Classification 1991: Primary 19B99, 19D99; secondary 18E10, 18F25. 相似文献
6.
The Frattini Subalgebra of Restricted Lie Superalgebras 总被引:6,自引:0,他引:6
Liang Yun CHEN Dao Ji MENG Yong Zheng ZHANG 《数学学报(英文版)》2006,22(5):1343-1356
In the present paper, we study the Frattini subalgebra of a restricted Lie superalgebra (L, [p]). We show first that if L = A1 + A2 +… +An, then Фp(L) = Фp(A1) +Фp(A2) +…+Фp(An), where each Ai is a p-ideal of L. We then obtain two results: F(L) = Ф(L) = J(L) = L if and only if L is nilpotent; Fp(L) and F(L) are nilpotent ideals of L if L is solvable. In addition, necessary and sufficient conditions are found for Фp-free restricted Lie superalgebras. Finally, we discuss the relationships of E-p-restricted Lie superalgebras and E-restricted Lie superalgebras. 相似文献
7.
J H Pathak 《Proceedings Mathematical Sciences》1989,99(3):217-220
LetA andB be two reduced commutative rings with finitely many minimal prime ideals. If the polynomial algebrasA[X
1
…X
n
]=B[Y
1
…Y
n
] whereX
i
,Y
iF are variables overA andB respectively, then there exists an injective ring homomorphism ϕ:A→B such thatB is finitely generated over ϕ(A). 相似文献
8.
Let T be a complete local (Noetherian) ring with maximal ideal M, P a nonmaximal ideal of T, and C = {Q 1, Q 2,…} a (nonempty) finite or countable set of nonmaximal prime ideals of T. Let {p 1, p 2,…} be a set of nonzero regular elements of T, whose cardinality is the same as that of C. Suppose that p i ∈ Q j if and only if i = j. We give conditions that ensure there is an excellent local unique factorization domain A such that A is a subring of T, the maximal ideal of A is M ∩ A, the (M ∩ A)-adic completion of A is T, and so that the following three conditions hold: (1) p i ∈ A for every i; (2) A ∩ P = (0), and if J is a prime ideal of T with J ∩ A = (0), then J ? P or J ? Q i for some i; (3) for each i, p i A is a prime ideal of A, Q i ∩ A = p i A, and if J is a prime ideal of T with J ? Q i , then J ∩ A ≠ p i A. 相似文献
9.
Eben Matlis 《Israel Journal of Mathematics》1980,37(3):211-230
LetR be an integral domain andI a non-zero ideal ofR. The canonical mapR→R/I is called atorsion-free cover ofR/I if everyR-homomorphism from a torsion-freeR-module intoR/I can be factored throughR. The main result of this paper is thatR→R/I is a torsion-free cover if and only ifR is complete in theR-topology andI is an ideal of injective dimension 1. In this caseI is contained in the Jacobson radical ofR. And if Λ is the endomorphism ring ofI, then Λ is a quasi-local domain. IfI is a flatR-module, thenQ→Q/Λ is a torsion-free cover, whereQ is the quotient field ofR. And thenQ/Λ is an indecomposable injectiveR (and Λ) module. Special results are obtained ifR is a Noetherian domain or a Prüfer domain. 相似文献
10.
11.
Consider the smooth quadric Q
6 in ℙ7. The middle homology group H
6(Q
6, ℤ) is isomorphic to ℤ ⊕ ℤ, with a basis given by two classes of linear subspaces. We classify all threefolds of bidegree
(1, p) inside Q
6. 相似文献
12.
Andrew H. Hoefel 《代数通讯》2013,41(4):1222-1233
Let P = 𝕜[x 1,…, x n ] be the polynomial ring in n variables. A homogeneous ideal I ? P generated in degree d is called Gotzmann if it has the smallest possible Hilbert function out of all homogeneous ideals with the same dimension in degree d. The edge ideal of a simple graph G on vertices x 1,…, x n is the quadratic square-free monomial ideal generated by all x i x j where {x i , x j } is an edge of G. The only edge ideals that are Gotzmann are those edge ideals corresponding to star graphs. 相似文献
13.
Walter Bergweiler 《Journal d'Analyse Mathématique》1994,63(1):121-129
Let (zj) be a sequence of complex numbers satisfying |zj|→ ∞ asj → ∞ and denote by n(r) the number of zj satisfying |zj|≤ r. Suppose that lim infr → ⇈ log n(r)/ logr > 0. Let ϕ be a positive, non-decreasing function satisfying ∫∞ (ϕ(t)t logt)−1
dt < ∞. It is proved that there exists an entire functionf whose zeros are the zj such that log log M(r,f) = o((log n(r))2ϕ(log n(r))) asr → ∞ outside some exceptional set of finite logarithmic measure, and that the integral condition on ϕ is best possible here.
These results answer a question by A. A. Gol’dberg. 相似文献
14.
Let G be a finite nonabelian group, ℤG its associated integral group ring, and Δ(G) its augmentation ideal. For the semidihedral group and another nonabelian 2-group the problem of their augmentation ideals
and quotient groups Q
n
(G) = Δ
n
(G)/Δ
n+1(G) is deal with. An explicit basis for the augmentation ideal is obtained, so that the structure of its quotient groups can
be determined. 相似文献
15.
Pekka Tukia 《Journal d'Analyse Mathématique》2006,99(1):35-87
We extend the results of [T2] to the situation where there is a compatibility with the action of a Kleinian group. A classical
Techmüller sequence is a sequence of quasiconformal mapsf
i with complex dilatations of the form
, where ϕ is a quadratic differential and 0<-k
i<1 are numbers such thatk
i→1 asi→∞. We proved in [T2] that if τ is a vertical trajectory associated to ϕ, then there is often, for instance if the sequence
is normalized so thatf
i fix 3 points, a subsequence such thatf
i tend either toward a constant or an injective map of τ. If there is compatibility with the action of a non-elementary finitely
generated Kleinian groupG, we can given a precise characterization which of these cases occurs. Suppose thatf
i induce isomorphisms ϕi ofG onto another Kleinian group and that ϕi have algebraic limit ϕ. If the quadratic differential is defined on a component of the ordinary set ofG, if there are no parabolic elements, and if τ is extended maximally so that all branches coming together at a singular point
are included, then we can state the main result as follows. The limit is a constantc if the stabilizerG
τ of τ is elementary; and, if it is non-elementary, then the limit is injective. In the first case, ϕ(g) is parabolic with fixpointc wheneverg∈G
τ is of infinite order; and in the latter case, the limitf is an embedding of τ in a natural topology of τ, andf embeds τ into a component of the limit set of ϕG whose stabilizer is ϕG
τ. Various extensions and generalizations are presented.
The research for this paper has been supported by the project 51749 of the Academy of Finland. 相似文献
16.
We consider the collision dynamics produced by three beads with masses (m
1, m
2, m
3) sliding without friction on a ring, where the masses are scaled so that m
1 = 1/ɛ, m
2 = 1, m
3 = 1 − ɛ, for 0 ⩽ ɛ ⩾ 1. The singular limits ɛ = 0 and ɛ = 1 correspond to two equal mass beads colliding on the ring with a wall, and without a wall respectively. In both these
cases, all solutions are periodic and the eigenvalue distributions (around the unit circle) associated with the products of
collision matrices are discrete. We then numerically examine the regime which parametrically connects these two states, i.e.
0 < ɛ < 1, and show that the eigenvalue distribution is generically uniform around the unit circle, which implies that the dynamics
are no longer periodic. By a sequence of careful numerical experiments, we characterize how the uniform spectrum collapses
from continuous to discrete in the two singular limits ɛ → 0 and ɛ → 1 for an ensemble of initial velocities sampled uniformly on a fixed energy surface. For the limit ɛ → 0, the distribution forms Gaussian peaks around the discrete limiting values ± 1, ± i, with variances that scale in power law form as σ
2 ∼ αɛ
β. By contrast, the convergence in the limit ɛ → 1 to the discrete values ±1 is shown to follow a logarithmic power-law σ
2 ∼ log(ɛ
β). 相似文献
17.
L. V. Rozovskii 《Vestnik St. Petersburg University: Mathematics》2011,44(2):129-133
Consider a sequence {X
i
} of independent copies of a nonnegative random variable X and let M = sup
j ≥ 1λ
j
X
j
, where {λ
j
} is a nonincreasing sequence of positive numbers for which P(M < ∞) = 1. The asymptotic behavior of -logP(M < r) as r → 0 is studied. 相似文献
18.
Graham Smith 《Geometriae Dedicata》2009,140(1):95-135
Let (M, Q) be a compact, three dimensional manifold of strictly negative sectional curvature. Let (Σ, P) be a compact, orientable surface of hyperbolic type (i.e. of genus at least two). Let θ : π1(Σ, P) → π1(M, Q) be a homomorphism. Generalising a recent result of Gallo, Kapovich and Marden concerning necessary and sufficient conditions
for the existence of complex projective structures with specified holonomy to manifolds of non-constant negative curvature,
we obtain necessary conditions on θ for the existence of a so called θ-equivariant Plateau problem over Σ, which is equivalent to the existence of a strictly convex immersion i : Σ → M which realises θ (i.e. such that θ = i
*).
相似文献
19.
Balázs Csikós György Kiss Konrad J. Swanepoel P. Oloff de Wet 《Periodica Mathematica Hungarica》2009,58(2):129-138
A family {A
i
| i ∈ I} of sets in ℝ
d
is antipodal if for any distinct i, j ∈ I and any p ∈ A
i
, q ∈ A
j
, there is a linear functional ϕ:ℝ
d
→ ℝ such that ϕ(p) ≠ ϕ(q) and ϕ(p) ≤ ϕ(r) ≤ ϕ(q) for all r ∈ ∪
i∈I
A
i
. We study the existence of antipodal families of large finite or infinite sets in ℝ3.
The research was supported by the Hungarian-South African Intergovernmental Scientific and Technological Cooperation Programme,
NKTH Grant no. ZA-21/2006 and South African National Research Foundation Grant no. UID 61853, as well as Hungarian National
Foundation for Scientific Research Grants no. NK 67867, no. T47102, and no. K72537. 相似文献
20.
D. V. Millionshchikov 《Proceedings of the Steklov Institute of Mathematics》2006,252(1):182-204
We study symplectic structures on filiform Lie algebras, which are niplotent Lie algebras with the maximal length of the descending
central sequence. Let g be a symplectic filiform Lie algebra and dim g = 2k ≥ 12. Then g is isomorphic to some ℕ-filtered deformation either of m0(2k) (defined by the structure relations [e
1, e
i
] = e
i+1, i = 2,…, 2k − 1) or of V
2k
, the quotient of the positive part of the Witt algebra W
+ by the ideal of elements of degree greater than 2k. We classify ℕ-filtered deformations of V
n
: [e
i
, e
j
] = (j − i)e
i+1 + Σ
l≥1
c
ij
l
e
i+j+l
. For dim g = n ≥ 16, the moduli space ℳn of these deformations is the weighted projective space
. For even n, the subspace of symplectic Lie algebras is determined by a single linear equation.
Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2006, Vol. 252, pp. 194–216. 相似文献