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1.
Every module over an Iwanaga–Gorenstein ring has a Gorenstein flat cover [13] (however, only a few nontrivial examples are
known). Integral group rings over polycyclic-by-finite groups are Iwanaga–Gorenstein [10] and so their modules have such covers.
In particular, modules over integral group rings of finite groups have these covers. In this article we initiate a study of
these covers over these group rings. To do so we study the so-called Gorenstein cotorsion modules, i.e. the modules that split
under Gorenstein flat modules. When the ring is ℤ, these are just the usual cotorsion modules. Harrison [16] gave a complete
characterization of torsion free cotorsion ℤ-modules. We show that with appropriate modifications Harrison's results carry
over to integral group rings ℤG when G is finite. So we classify the Gorenstein cotorsion modules which are also Gorenstein flat over these ℤG. Using these results we classify modules that can be the kernels of Gorenstein flat covers of integral group rings of finite
groups. In so doing we necessarily give examples of such covers. We use the tools we develop to associate an integer invariant
n with every finite group G and prime p. We show 1≤n≤|G : P| where P is a Sylow p-subgroup of G and gives some indication of the significance of this invariant. We also use the results of the paper to describe the co-Galois
groups associated to the Gorenstein flat cover of a ℤG-module.
Presented by A. Verschoren
Mathematics Subject Classifications (2000) 20C05, 16E65. 相似文献
2.
A. M. Samoilenko V. G. Samoilenko Yu. M. Sidorenko 《Ukrainian Mathematical Journal》1999,51(1):86-106
We present a spatially two-dimensional generalization of the hierarchy of Kadomtsev-Petviashvili equations under nonlocal
constraints (the so-called 2-dimensionalk-constrained KP-hierarchy, briefly called the 2d k-c-hierarchy). As examples of (2+1)-dimensional nonlinear models belonging to the 2d k-c KP-hierarchy, both generalizations of already known systems and new nonlinear systems are presented. A method for the construction
of exact solutions of equations belonging to the 2d k-c KP-hierarchy is proposed.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 1, pp. 78–97, January, 1999. 相似文献
3.
P. M. Akhmet’ev 《Journal of Mathematical Sciences》2009,159(6):761-776
We present an approach to the Kervaire-invariant-one problem. The notion of the geometric (ℤ/2 ⨁ ℤ/2)-control of self-intersection of a skew-framed immersion and the notion of the (ℤ/2 ⨁ ℤ/4)-structure on the self-intersection manifold of a D
4-framed immersion are introduced. It is shown that a skew-framed immersion ↬ℝ
n
, 0 < q ≪ n (in the -range), admits a geometric (ℤ/2 ⨁ ℤ/2)-control if the characteristic class of the skew-framing of this immersion admits a retraction of order q, i.e., there exists a mapping such that this composition → ℝP∞ is the characteristic class of the skew-framing of f. Using the notion of (ℤ/2 ⨁ ℤ/2)-control, we prove that for a sufficiently large n, n = 2
l
− 2, an arbitrarily immersed D
4-framed manifold admits in the regular cobordism class (modulo odd torsion) an immersion with a (ℤ/2 ⨁ ℤ/4)-structure.
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 8, pp. 17–41, 2007. 相似文献
4.
We consider Toda equations associated with twisted loop groups. Such equations are specified by ℤ-gradings of the corresponding
twisted loop Lie algebras. We discuss the classification of Toda equations related to twisted loop Lie algebras with integrable
ℤ-gradings.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 3, pp. 451–476, March, 2008. 相似文献
5.
Morten Nielsen 《Advances in Computational Mathematics》2007,27(2):195-209
Given a dilation matrix A :ℤd→ℤd, and G a complete set of coset representatives of 2π(A
−Tℤd/ℤd), we consider polynomial solutions M to the equation ∑
g∈G
M(ξ+g)=1 with the constraints that M≥0 and M(0)=1. We prove that the full class of such functions can be generated using polynomial convolution kernels. Trigonometric
polynomials of this type play an important role as symbols for interpolatory subdivision schemes. For isotropic dilation matrices,
we use the method introduced to construct symbols for interpolatory subdivision schemes satisfying Strang–Fix conditions of
arbitrary order.
Research partially supported by the Danish Technical Science Foundation, Grant No. 9701481, and by the Danish SNF-PDE network. 相似文献
6.
An irreducible algebraic ℤ
d
-actionα on a compact abelian group X is a ℤ
d
-action by automorphisms of X such that every closed, α-invariant subgroup Y⊊X is finite. We prove the following result: if d≥2, then every measurable conjugacy between irreducible and mixing algebraic ℤ
d
-actions on compact zero-dimensional abelian groups is affine. For irreducible, expansive and mixing algebraic ℤ
d
-actions on compact connected abelian groups the analogous statement follows essentially from a result by Katok and Spatzier
on invariant measures of such actions (cf. [4] and [3]). By combining these two theorems one obtains isomorphism rigidity
of all irreducible, expansive and mixing algebraic ℤ
d
-actions with d≥2.
Oblatum 30-IX-1999 & 4-V-2000?Published online: 16 August 2000 相似文献
7.
Multi‐component integrable couplings for the Ablowitz–Kaup–Newell–Segur and Volterra hierarchies 下载免费PDF全文
Shoufeng Shen Chunxia Li Yongyang Jin Shuimeng Yu 《Mathematical Methods in the Applied Sciences》2015,38(17):4345-4356
A kind of N × N non‐semisimple Lie algebra consisting of triangular block matrices is used to generate multi‐component integrable couplings of soliton hierarchies from zero curvature equations. Two illustrative examples are made for the continuous Ablowitz–Kaup–Newell–Segur hierarchy and the semi‐discrete Volterra hierarchy, together with recursion operators. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
8.
L. A. Gilch 《Journal of Mathematical Sciences》2009,156(1):173-186
Suppose we are given a homogeneous tree {ie173-01} of degree q ≥ 3, where at each vertex sits a lamp, which can be switched on or off. This structure can be described by the wreath product
(ℤ/2)≀Γ, where Γ = *
i=1qℤ/2 is the free product group of q factors ℤ/2. We consider a transient random walk on a Cayley graph of (ℤ/2) ≀Γ, for which we want to compute lower and upper
bounds for the rate of escape, that is, the speed at which the random walk flees to infinity.
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 50, Functional
Analysis, 2007. 相似文献
9.
T. E. Panov 《Mathematical Notes》1998,63(2):225-232
We deal with quasi-complex manifolds with an action of the group ℤ/p such that the set of fixed points of this action has a trivial normal bundle. The set of cobordism classes of these manifolds
is described in terms of the coefficients of the formal group of geometric cobordisms and in terms of characteristic numbers.
We also establish the relationship between this work and relevant papers containing a solution of this problem in some particular
cases.
Translated fromMatematicheskie Zametki, Vol. 63, No. 2, pp. 260–268, February, 1998.
The author is greatly indebted to his advisor Professor V. M. Bukhshtaber for his active interest in this work and useful
discussions.
This research was supported by the Russian Foundation for Basic Research under grant No. 96-01-01404. 相似文献
10.
Abdelmalek Azizi 《Rendiconti del Circolo Matematico di Palermo》1999,48(1):71-92
Let ℕ,i=√−1,k=ℚ(√d,i) andC
2 the 2-part of the class group ofk. Our goal is to determine alld such thatC
2⋍ℤ/2ℤ×ℤ/2ℤ.
Soientd∈ℕ,i=√−1,k=ℚ(√d,i), etC
2 la 2-partie du groupe de classes dek. On s'intéresse à déterminer tous lesd tel queC
2⋍ℤ/2ℤ×ℤ/2ℤ.
相似文献
11.
Paul Arne ?stv?r 《K-Theory》2004,31(4):345-355
Let X be a connected based space and p be a two-regular prime number. If the fundamental group of X has order p, we compute the two-primary homotopy groups of the homotopy fiber of the trace map A(X) → TC(X) relating algebraic K-theory of spaces to topological cyclic homology. The proof uses a theorem of Dundas and an explicit calculation of the cyclotomic
trace map K(ℤ[Cp])→ TC(ℤ[Cp]). 相似文献
12.
V. V. Gribanov V. G. Kadyshevsky A. S. Sorin 《Theoretical and Mathematical Physics》2006,146(1):73-84
By exhibiting the corresponding Lax-pair representations, we propose a wide class of integrable two-dimensional (2D) fermionic
Toda lattice (TL) hierarchies, which includes the 2D N=(2|2) and N=(0|2) supersymmetric TL hierarchies as particular cases.
We develop the generalized graded R-matrix formalism using the generalized graded bracket on the space of graded operators
with involution generalizing the graded commutator in superalgebras, which allows describing these hierarchies in the framework
of the Hamiltonian formalism and constructing their first two Hamiltonian structures. We obtain the first Hamiltonian structure
for both bosonic and fermionic Lax operators and the second Hamiltonian structure only for bosonic Lax operators.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 1, pp. 90–102, January, 2006. 相似文献
13.
Antônio BrandãoJr. 《Rendiconti del Circolo Matematico di Palermo》2008,57(2):265-278
Let M
n
(K) be the algebra of all n × n matrices over an infinite field K. This algebra has a natural ℤ
n
-grading and a natural ℤ-grading. Finite bases for its ℤ
n
-graded identities and for its ℤ-graded identities are known. In this paper we describe finite generating sets for the ℤ
n
-graded and for the ℤ-graded central polynomials for M
n
(K)
Partially supported by CNPq 620025/2006-9 相似文献
14.
Yan-Bo Yuan 《Acta Appl Math》2008,104(2):151-159
Let μ
R,D
be a self-affine measure associated with an expanding integer matrix R∈M
n
(ℤ) and a finite subset D⊆ℤ
n
. In the present paper we study the μ
R,D
-orthogonality and compatible pair conditions. We also show that any set of μ
R,D
-orthogonal exponentials contains at most 3 elements on the generalized plane Sierpinski gasket and the number 3 is the best.
相似文献
15.
Mathieu Florence 《Inventiones Mathematicae》2008,171(1):175-189
Let p be a prime number, let K be a field of characteristic not p, containing the p-th roots of unity, and let r≥1 be an integer. We compute the essential dimension of ℤ/p
r
ℤ over K (Theorem 4.1). In particular,
i) We have edℚ(ℤ/8ℤ)=4, a result which was conjectured by Buhler and Reichstein in 1995 (unpublished).
ii) We have edℚ(ℤ/p
r
ℤ)≥p
r-1. 相似文献
16.
T. O. Banach 《Mathematical Notes》1998,64(3):295-302
For each Abelian groupG, a cardinal invariant χ(G) is introduced and its properties are studied. In the special caseG = ℤ
n
, the cardinalχ(ℤ
n
) is equal to the minimal cardinality of an essential subset of ℤ
n
, i.e., a of a subsetA ⊂ ℤ
n
such that, for any coloring of the group ℤ
n
inn colors, there exists an infinite one-color subset that is symmetric with respect to some pointα ofA. The estimaten(
n + l)/2 ≤χ(ℤ
n
) < 2n is proved for alln and the relationχ(ℤ
n
) =n(n + 1)/2 forn ≤ 3. The structure of essential subsets of cardinalityχ(ℤ
n
) in ℤ
n
is completely described forn ≤ 3.
Translated fromMatematicheskie Zametki, Vol. 64, No. 3, pp. 341–350, September, 1998. 相似文献
17.
Wolfgang A. Schmid 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2009,79(1):25-35
Let H be a Krull monoid with finite class group such that each class contains a prime divisor (e.g., the multiplicative monoid
of the ring of algebraic integers of some number field). It is shown that it can be determined whether the class group is
of the form ℤ/nℤ⊕ℤ/nℤ, for n≥3, just by considering the system of sets of lengths of H.
Supported by the Austrian Science Fund FWF (Project P18779-N13). 相似文献
18.
A. Vourdas 《Journal of Fourier Analysis and Applications》2010,16(5):748-767
Harmonic analysis on ℤ(p
ℓ
) and the corresponding representation of the Heisenberg-Weyl group HW[ℤ(p
ℓ
),ℤ(p
ℓ
),ℤ(p
ℓ
)], is studied. It is shown that the HW[ℤ(p
ℓ
),ℤ(p
ℓ
),ℤ(p
ℓ
)] with a homomorphism between them, form an inverse system which has as inverse limit the profinite representation of the
Heisenberg-Weyl group
\mathfrak HW[\mathbbZp,\mathbbZp,\mathbbZp]\mathfrak {HW}[{\mathbb{Z}}_{p},{\mathbb{Z}}_{p},{\mathbb{Z}}_{p}]. Harmonic analysis on ℤ
p
is also studied. The corresponding representation of the Heisenberg-Weyl group HW[(ℚ
p
/ℤ
p
),ℤ
p
,(ℚ
p
/ℤ
p
)] is a totally disconnected and locally compact topological group. 相似文献
19.
A refinable spline in ℝ
d
is a compactly supported refinable function whose support can be decomposed into simplices such that the function is a polynomial
on each simplex. The best-known refinable splines in ℝ
d
are the box splines. Refinable splines play a key role in many applications, such as numerical computation, approximation
theory and computer-aided geometric design. Such functions have been classified in one dimension in Dai et al. (Appl. Comput.
Harmon. Anal. 22(3), 374–381, 2007), Lawton et al. (Comput. Math. 3, 137–145, 1995). In higher dimensions Sun (J. Approx. Theory 86, 240–252, 1996) characterized those splines when the dilation matrices are of the form A=mI, where m∈ℤ and I is the identity matrix. For more general dilation matrices the problem becomes more complex. In this paper we give a complete
classification of refinable splines in ℝ
d
for arbitrary dilation matrices A∈M
d
(ℤ). 相似文献
20.
The authors give finite dimensional exponential solutions of the bigraded Toda hierarchy (BTH). As a specific example of exponential solutions of the BTH, the authors consider a regular solution for the (1, 2)-BTH with a 3 × 3-sized Lax matrix, and discuss some geometric structures of the solution from which the difference between the (1, 2)- BTH and the original Toda hierarchy is shown. After this, the authors construct another kind of Lax representation of (N, 1)-BTH which does not use the fractional operator of Lax operator. Then the authors introduce the lattice Miura transformation of (N, 1)-BTH which leads to equations depending on one field, and meanwhile some specific examples which contain the Volterra lattice equation (a useful ecological competition model) are given. 相似文献