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1.
We prove that every compact nilpotent ring R of characteristic p > 0 can be embedded in a ring of upper triangular matrices over a compact commutative ring. Furthermore, we prove that every
compact topologically nilpotent ring R of characteristic p > 0, is embedded in a ring of infinite triangular matrices over
\mathbbFpw(R)\mathbb{F}_{p}^{w(R)}. 相似文献
2.
Let μ be a Poisson random measure, let
\mathbbF\mathbb{F} be the smallest filtration satisfying the usual conditions and containing the one generated by μ, and let
\mathbbG\mathbb{G} be the initial enlargement of
\mathbbF\mathbb{F} with the σ-field generated by a random variable G. In this paper, we first show that the mutual information between the enlarging random variable G and the σ-algebra generated by the Poisson random measure μ is equal to the expected relative entropy of the
\mathbbG\mathbb{G}-compensator relative to the
\mathbbF\mathbb{F}-compensator of the random measure μ. We then use this link to gain some insight into the changes of Doob–Meyer decompositions of stochastic processes when the
filtration is enlarged from
\mathbbF\mathbb{F} to
\mathbbG\mathbb{G}. In particular, we show that if the mutual information between G and the σ-algebra generated by the Poisson random measure μ is finite, then every square-integrable
\mathbbF\mathbb{F}-martingale is a
\mathbbG\mathbb{G}-semimartingale that belongs to the normed space S1\mathcal{S}^{1} relative to
\mathbbG\mathbb{G}. 相似文献
3.
Transitive Permutation Groups of Prime-Squared Degree 总被引:2,自引:0,他引:2
4.
O. Yu. Dashkova 《Ukrainian Mathematical Journal》2012,63(9):1379-1389
We study a
\mathbbZG \mathbb{Z}G -module A such that
\mathbbZ \mathbb{Z} is the ring of integer numbers, the group G has an infinite sectional p-rank (or an infinite 0-rank), C
G
(A) = 1, A is not a minimax
\mathbbZ \mathbb{Z} -module, and, for any proper subgroup H of infinite sectional p-rank (or infinite 0-rank, respectively), the quotient module A/C
A
(H) is a minimax
\mathbbZ \mathbb{Z} -module. It is shown that if the group G is locally soluble, then it is soluble. Some properties of soluble groups of this kind are discussed. 相似文献
5.
We describe the dynamics of an arbitrary affine dynamical system on a local field by exhibiting all its minimal subsystems.
In the special case of the field
\mathbbQp{\mathbb{Q}_p} of p-adic numbers, for any non-trivial affine dynamical system, we prove that the field
\mathbbQp{\mathbb{Q}_p} is decomposed into a countable number of invariant balls or spheres each of which consists of a finite number of minimal
subsets. Consequently, we give a complete classification of topological conjugacy for non-trivial affine dynamics on
\mathbbQp{\mathbb{Q}_p} . For each given prime p, there is a finite number of conjugacy classes. 相似文献
6.
7.
Boris Širola 《Central European Journal of Mathematics》2011,9(6):1317-1332
Let
\mathbbK\mathbb{K} be a field, G a reductive algebraic
\mathbbK\mathbb{K}-group, and G
1 ≤ G a reductive subgroup. For G
1 ≤ G, the corresponding groups of
\mathbbK\mathbb{K}-points, we study the normalizer N = N
G
(G
1). In particular, for a standard embedding of the odd orthogonal group G
1 = SO(m,
\mathbbK\mathbb{K}) in G = SL(m,
\mathbbK\mathbb{K}) we have N ≅ G
1 ⋊ μ
m
(
\mathbbK\mathbb{K}), the semidirect product of G
1 by the group of m-th roots of unity in
\mathbbK\mathbb{K}. The normalizers of the even orthogonal and symplectic subgroup of SL(2n,
\mathbbK\mathbb{K}) were computed in [Širola B., Normalizers and self-normalizing subgroups, Glas. Mat. Ser. III (in press)], leaving the proof
in the odd orthogonal case to be completed here. Also, for G = GL(m,
\mathbbK\mathbb{K}) and G
1 = O(m,
\mathbbK\mathbb{K}) we have N ≅ G
1 ⋊
\mathbbK\mathbb{K}
×. In both of these cases, N is a self-normalizing subgroup of G. 相似文献
8.
A. N. Khisamiev 《Algebra and Logic》2012,51(1):89-102
We construct a family of Σ-uniform Abelian groups and a family of Σ-uniform rings. Conditions are specified that are necessary and sufficient for a universal Σ-function to exist in a hereditarily finite admissible set over structures in these families. It is proved that there is a set S of primes such that no universal Σ-function exists in hereditarily finite admissible sets \mathbbH\mathbbF(G) \mathbb{H}\mathbb{F}(G) and \mathbbH\mathbbF(K) \mathbb{H}\mathbb{F}(K) , where G = ⊕{Z p | p ∈ S} is a group, Z p is a cyclic group of order p, K = ⊕{F p | p ∈ S} is a ring, and F p is a prime field of characteristic p. 相似文献
9.
Swarnendu Datta 《Transformation Groups》2010,15(1):72-91
Let G be a commutative, unipotent, perfect, connected group scheme over an algebraically closed field of characteristic p > 0 and let E be a biextension of G × G by the discrete group
\mathbbQp/\mathbbZp\mathbb{Q}_{p}/\mathbb{Z}_{p}. When E is skew-symmetric, V. Drinfeld defined a certain metric group A associated to E (when G is the perfectization of the additive group
\mathbbGa\mathbb{G}_{a}, it is easy to compute this metric group, cf. Appendix A). In this paper we prove a conjecture due to Drinfeld about the
class of the metric group A in the Witt group (cf. Appendix B). 相似文献
10.
Chris Woodcock 《Journal of Pure and Applied Algebra》2007,210(1):193-199
Throughout, all rings R will be commutative with identity element. In this paper we introduce, for each finite group G, a commutative graded Z-algebra RG. This classifies the G-invariant commutative R-algebra multiplications on the group algebra R[G] which are cocycles (in fact coboundaries) with respect to the standard “direct sum” multiplication and have the same identity element.In the case when G is an elementary Abelian p-group it turns out that RG is closely related to the symmetric algebra over Fp of the dual of G. We intend in subsequent papers to explore the close relationship between G and RG in the case of a general (possibly non-Abelian) group G.Here we show that the Krull dimension of RG is the maximal rank r of an elementary Abelian subgroup E of G unless either E is cyclic or for some such E its normalizer in G contains a non-trivial cyclic group which acts faithfully on E via “scalar multiplication” in which case it is r+1. 相似文献
11.
For n = 1, the space of ${\mathbb{R}}For n = 1, the space of
\mathbbR{\mathbb{R}} -places of the rational function field
\mathbbR(x1,?, xn){\mathbb{R}(x_1,\ldots, x_n)} is homeomorphic to the real projective line. For n ≥ 2, the structure is much more complicated. We prove that the space of
\mathbbR{\mathbb{R}} -places of the rational function field
\mathbbR(x, y){\mathbb{R}(x, y)} is not metrizable. We explain how the proof generalizes to show that the space of
\mathbbR{\mathbb{R}} -places of any finitely generated formally real field extension of
\mathbbR{\mathbb{R}} of transcendence degree ≥ 2 is not metrizable. We also consider the more general question of when the space of
\mathbbR{\mathbb{R}} -places of a finitely generated formally real field extension of a real closed field is metrizable. 相似文献
12.
A. S. Morozov 《Algebra and Logic》2012,51(1):66-88
It is proved that every two Σ-presentations of an ordered field \mathbbR \mathbb{R} of reals over \mathbbH\mathbbF ( \mathbbR ) \mathbb{H}\mathbb{F}\,\left( \mathbb{R} \right) , whose universes are subsets of \mathbbR \mathbb{R} , are mutually Σ-isomorphic. As a consequence, for a series of functions f:\mathbbR ? \mathbbR f:\mathbb{R} \to \mathbb{R} (e.g., exp, sin, cos, ln), it is stated that the structure \mathbbR \mathbb{R} = 〈R, +, ×, <, 0, 1, f〉 lacks such Σ-presentations over \mathbbH\mathbbF ( \mathbbR ) \mathbb{H}\mathbb{F}\,\left( \mathbb{R} \right) . 相似文献
13.
Mahmoud Baroun Lahcen Maniar Roland Schnaubelt 《Integral Equations and Operator Theory》2009,65(2):169-193
We show the existence and uniqueness of the (asymptotically) almost periodic solution to parabolic evolution equations with
inhomogeneous boundary values on
\mathbbR{\mathbb{R}} and
\mathbbR±\mathbb{R}_{\pm}, if the data are (asymptotically) almost periodic. We assume that the underlying homogeneous problem satisfies the ‘Acquistapace–Terreni’
conditions and has an exponential dichotomy. If there is an exponential dichotomy only on half intervals ( − ∞, − T] and [T, ∞), then we obtain a Fredholm alternative of the equation on
\mathbbR{\mathbb{R}} in the space of functions being asymptotically almost periodic on
\mathbbR+{\mathbb{R}}_{+} and
\mathbbR-\mathbb{R}_{-}. 相似文献
14.
We use properties of small resolutions of the ordinary double point in dimension three to construct smooth non-liftable Calabi-Yau
threefolds. In particular, we construct a smooth projective Calabi-Yau threefold over
\mathbbF3{\mathbb{F}_3} that does not lift to characteristic zero and a smooth projective Calabi-Yau threefold over
\mathbbF5{\mathbb{F}_5} having an obstructed deformation. We also construct many examples of smooth Calabi-Yau algebraic spaces over
\mathbbFp{\mathbb{F}_p} that do not lift to algebraic spaces in characteristic zero. 相似文献
15.
For any category of interest ℂ we define a general category of groups with operations
\mathbbCG, \mathbbC\hookrightarrow\mathbbCG\mathbb{C_G}, \mathbb{C}\hookrightarrow\mathbb{C_G}, and a universal strict general actor USGA(A) of an object A in ℂ, which is an object of
\mathbbCG\mathbb{C_G}. The notion of actor is equivalent to the one of split extension classifier defined for an object in more general settings
of semi-abelian categories. It is proved that there exists an actor of A in ℂ if and only if the semidirect product
\textUSGA(A)\ltimes A{\text{USGA}}(A)\ltimes A is an object of ℂ and if it is the case, then USGA(A) is an actor of A. We give a construction of a universal strict general actor for any A ∈ ℂ, which helps to detect more properties of this object. The cases of groups, Lie, Leibniz, associative, commutative associative,
alternative algebras, crossed and precrossed modules are considered. The examples of algebras are given, for which always
exist actors. 相似文献
16.
We determine which singular del Pezzo surfaces are equivariant compactifications of
\mathbbG\texta2 \mathbb{G}_{\text{a}}^2 , to assist with proofs of Manin’s conjecture for such surfaces. Additionally, we give an example of a singular quartic del
Pezzo surface that is an equivariant compactification of
\mathbbG\texta {\mathbb{G}_{\text{a}}} ⋊
\mathbbG\textm {\mathbb{G}_{\text{m}}} . Bibliography: 32 titles. 相似文献
17.
We study maximal L
p
-regularity for a class of pseudodifferential mixed-order systems on a space–time cylinder
\mathbbRn ×\mathbbR{\mathbb{R}^n \times \mathbb{R}} or
X ×\mathbbR{X \times \mathbb{R}} , where X is a closed smooth manifold. To this end, we construct a calculus of Volterra pseudodifferential operators and characterize
the parabolicity of a system by the invertibility of certain associated symbols. A parabolic system is shown to induce isomorphisms
between suitable L
p
-Sobolev spaces of Bessel potential or Besov type. If the cross section of the space–time cylinder is compact, the inverse
of a parabolic system belongs to the calculus again. As applications, we discuss time-dependent Douglis–Nirenberg systems
and a linear system arising in the study of the Stefan problem with Gibbs–Thomson correction. 相似文献
18.
Let
\mathbbZpm \mathbb{Z}_{p^m } be the ring of integers modulo p
m
, where p is a prime and m ⩾ 1. The general linear group GL
n
(
\mathbbZpm \mathbb{Z}_{p^m } ) acts naturally on the polynomial algebra A
n
:=
\mathbbZpm \mathbb{Z}_{p^m } [x
1, …, x
n
]. Denote by
AnGL2 (\mathbbZpm ) A_n^{GL_2 (\mathbb{Z}_{p^m } )} the corresponding ring of invariants. The purpose of the present paper is to calculate this invariant ring. Our results also
generalize the classical Dickson’s theorem. 相似文献
19.
G. Kutyniok 《Archiv der Mathematik》2002,78(2):135-144
Let
r\mathbbR \rho_{\mathbb{R}} be the classical Schrödinger representation of the Heisenberg group and let L \Lambda be a finite subset of
\mathbbR ×\mathbbR \mathbb{R} \times \mathbb{R} . The question of when the set of functions
{t ? e2 pi y t f(t + x) = (r\mathbbR(x, y, 1) f)(t) : (x, y) ? L} \{t \mapsto e^{2 \pi i y t} f(t + x) = (\rho_{\mathbb{R}}(x, y, 1) f)(t) : (x, y) \in \Lambda\} is linearly independent for all
f ? L2(\mathbbR), f 1 0 f \in L^2(\mathbb{R}), f \neq 0 , arises from Gabor analysis. We investigate an analogous problem for locally compact abelian groups G. For a finite subset L \Lambda of G ×[^(G)] G \times \widehat{G} and rG \rho_G the Schrödinger representation of the Heisenberg group associated with G, we give a necessary and in many situations also sufficient condition for the set {rG (x, w, 1)f : (x, w) ? L} \{\rho_G (x, w, 1)f : (x, w) \in \Lambda\} to be linearly independent for all f ? L2(G), f 1 0 f \in L^2(G), f \neq 0 . 相似文献
20.
Juan A. Aledo Victorino Lozano José A. Pastor 《Mediterranean Journal of Mathematics》2010,7(3):263-270
We prove that the only compact surfaces of positive constant Gaussian curvature in
\mathbbH2×\mathbbR{\mathbb{H}^{2}\times\mathbb{R}} (resp. positive constant Gaussian curvature greater than 1 in
\mathbbS2×\mathbbR{\mathbb{S}^{2}\times\mathbb{R}}) whose boundary Γ is contained in a slice of the ambient space and such that the surface intersects this slice at a constant
angle along Γ, are the pieces of a rotational complete surface. We also obtain some area estimates for surfaces of positive
constant Gaussian curvature in
\mathbbH2×\mathbbR{\mathbb{H}^{2}\times\mathbb{R}} and positive constant Gaussian curvature greater than 1 in
\mathbbS2×\mathbbR{\mathbb{S}^{2}\times\mathbb{R}} whose boundary is contained in a slice of the ambient space. These estimates are optimal in the sense that if the bounds
are attained, the surface is again a piece of a rotational complete surface. 相似文献