共查询到20条相似文献,搜索用时 721 毫秒
1.
Kenji Nishida 《Algebras and Representation Theory》2006,9(1):13-31
We generalize results of Foxby concerning a commutative Nötherian ring to a certain noncommutative Nötherian algebra Λ over a commutative Gorenstein complete local ring. We assume that Λ is a Cohen–Macaulay isolated singularity having a dualizing module. Then the same method as in the commutative cases works and we obtain a category equivalence between two subcategories of mod Λ, one of which includes all finitely generated modules of finite Gorenstein dimension. We give examples of such algebras which are not Gorenstien; orders related to almost Bass orders and some k-Gorenstein algebras for an integer k.Presented by I. Reiten
★The author is supported by Grant-in-Aid for Scientific Researches B(1) No. 14340007 in Japan. 相似文献
2.
Jun-ichi Miyachi 《Archiv der Mathematik》2006,86(4):317-320
Let Λ be a left Artinian ring, D+(mod Λ) (resp., D−(mod Λ), D(mod Λ)) the derived category of bounded below complexes (resp., bounded above complexes, unbounded complexes) of
finitely generated left Λ-modules. We show that the Grothendieck groups K0(D+(mod Λ)), K0(D−(mod Λ)) and K0(D(mod Λ)) are trivial.
Received: 7 April 2005 相似文献
3.
We consider the algebras Λ which satisfy the property that for each indecomposable module X, either its projective dimension pdΛ
X is at most one or its injective dimension idΛ
X is at most one. This clearly generalizes the so-called quasitilted algebras introduced by Happel–Reiten–Smal?. We show that
some of the niciest features for this latter class of algebras can be generalized to the case we are considering, in particular
the existence of a trisection in its module category.
Received: 26 August 1998 相似文献
4.
Otmar Venjakob 《Journal of the European Mathematical Society》2002,4(3):271-311
This paper is motivated by the question whether there is a nice structure theory of finitely generated modules over the Iwasawa
algebra, i.e. the completed group algebra, Λ of a p-adic analytic group G. For G without any p-torsion element we prove that Λ is an Auslander regular ring. This result enables us to give a good definition of the notion
of a pseudo-nullΛ-module. This is classical when G=ℤ
k
p
for some integer k≥1, but was previously unknown in the non-commutative case. Then the category of Λ-modules up to pseudo-isomorphisms is studied
and we obtain a weak structure theorem for the ℤ
p
-torsion part of a finitely generated Λ-module. We also prove a local duality theorem and a version of Auslander-Buchsbaum
equality. The arithmetic applications to the Iwasawa theory of abelian varieties are published elsewhere.
Received May 12, 2001 / final version received July 5, 2001?Published online September 3, 2001 相似文献
5.
Miguel Angel Javaloyes Levi Lopes de Lima Paolo Piccione 《Mathematische Zeitschrift》2008,260(2):277-303
Following the lines of Bott in (Commun Pure Appl Math 9:171–206, 1956), we study the Morse index of the iterates of a closed
geodesic in stationary Lorentzian manifolds, or, more generally, of a closed Lorentzian geodesic that admits a timelike periodic
Jacobi field. Given one such closed geodesic γ, we prove the existence of a locally constant integer valued map Λγ on the unit circle with the property that the Morse index of the iterated γ
N
is equal, up to a correction term εγ∈{0,1}, to the sum of the values of Λγ at the N-th roots of unity. The discontinuities of Λγ occur at a finite number of points of the unit circle, that are special eigenvalues of the linearized Poincaré map of γ.
We discuss some applications of the theory. 相似文献
6.
Oliver Lorscheid 《Archiv der Mathematik》2007,88(4):344-348
This paper shows that for a local field K, a subfield k ⊂ K and a variety X over k, X is complete if and only if for every finite field extension Kʹ | K, the set X(Kʹ) is compact in its strong topology.
The author likes to thank Florian Pop, Jakob Stix, Stefan Wewers, Gunther Cornelissen and his own parents for their support.
Received: 13 April 2006 相似文献
7.
Let k(x) be the field of fractions of the polynomial algebra k[x] over the field k. We prove that, for an arbitrary finite dimensional k-algebra Λ, any finitely generated Λ ⊗k k(x)-module M such that its minimal projective presentation admits no non-trivial selfextension is of the form M ≅ Nk(x), for some finitely generated Λ-module N. Some consequences are derived for tilting modules over the rational algebra Λ ⊗k k(x) and for some generic modules for Λ.
Received: 24 November 2003; revised: 11 February 2005 相似文献
8.
Raymundo Bautista Yuriy A. Drozd Xiangyong Zeng Yingbo Zhang 《Central European Journal of Mathematics》2007,5(2):215-263
Let Λ be a finite dimensional algebra over an algebraically closed field k and Λ has tame representation type. In this paper, the structure of Hom-spaces of all pairs of indecomposable Λ-modules having
dimension smaller than or equal to a fixed natural number is described, and their dimensions are calculated in terms of a
finite number of finitely generated Λ-modules and generic Λ-modules. In particular, such spaces are essentially controlled
by those of the corresponding generic modules.
The first author thanks the support of project “43374F” of Fondo Sectorial SEP-Conacyt. Y. Zhang thanks the support of Important
project 10331030 of Natural Science Foundation of China. 相似文献
9.
We show that a compact, connected set which has uniform oscillations at all points and at all scales has dimension strictly
larger than 1. We also show that limit sets of certain Kleinian groups have this property. More generally, we show that ifG is a non-elementary, analytically finite Kleinian group, and its limit set Λ(G) is connected, then Λ(G) is either a circle or has dimension strictly bigger than 1.
The first author is partially supported by NSF Grant DMS 95-00577 and an Alfred P. Sloan research fellowship. The second author
is partially supported by NSF grant DMS-94-23746. 相似文献
10.
It is shown that an algebra Λ can be lifted with nilpotent Jacobson radical r = r(Λ) and has a generalized matrix unit {e
ii
}
I
with each ē
ii
in the center of if Λ is isomorphic to a generalized path algebra with weak relations. Representations of the generalized path algebras are given.
As a corollary, Λ is a finite algebra with non-zero unity element over a perfect field k (e.g., a field with characteristic zero or a finite field) if Λ is isomorphic to a generalized path algebra k (D, Ω, ρ) of finite directed graph with weak relations and dim < ∞; Λ is a generalized elementary algebra which can be lifted with nilpotent Jacobson radical and has a complete set of pairwise
orthogonal idempotents if Λ is isomorphic to a path algebra with relations.
Presented by Idun Reiten. 相似文献
11.
Summary We prove that given a Noetherian ringR and a finitely generatedR-inoduleM, there exists a finite set of prime idealsΛ inR such that the depth of an arbitrary idealI onM is determined by the height ofI modulo each of the primes inΛ. As an application we answer a question raised by the second author and V. Srinivas concerning m-adic approximations of regular
sequences in a local ring.
This article was processed by the author using the Springer-Verlag TEX P Jourlg macro package 1991. 相似文献
12.
We show the relative consistency of ℵ1 satisfying a combinatorial property considered by David Fremlin (in the question DU from his list) in certain choiceless
inner models. This is demonstrated by first proving the property is true for Ramsey cardinals. In contrast, we show that in
ZFC, no cardinal of uncountable cofinality can satisfy a similar, stronger property. The questions considered by D. H. Fremlin
are if families of finite subsets of ω1 satisfying a certain density condition necessarily contain all finite subsets of an infinite subset of ω1, and specifically if this and a stronger property hold under MA + ?CH. Towards this we show that if MA + ?CH holds, then for every family ? of ℵ1 many infinite subsets of ω1, one can find a family ? of finite subsets of ω1 which is dense in Fremlins sense, and does not contain all finite subsets of any set in ?.
We then pose some open problems related to the question.
Received: 2 June 1999 / Revised version: 2 February 2000 / Published online: 18 July 2001 相似文献
13.
According to A. Beurling and H. Landau, if an exponential system {e
iλt
}λ∈Λ is a frame in L
2 on a set S of positive measure, then Λ must satisfy a strong density condition. We replace the frame concept by a weaker condition and
prove that if S is a finite union of segments then the result holds. However, for “generic” S, very sparse sequences Λ are admitted.
Supported in part by the Israel Science Foundation. 相似文献
14.
Mihail N. Kolountzakis 《Journal of Fourier Analysis and Applications》2012,18(1):21-26
A set Ω, of Lebesgue measure 1, in the real line is called spectral if there is a set Λ of real numbers such that the exponential
functions e
λ
(x)=exp (2πiλx), λ∈Λ, form a complete orthonormal system on L
2(Ω). Such a set Λ is called a spectrum of Ω. In this note we present a simplified proof of the fact that any spectrum Λ of
a set Ω which is finite union of intervals must be periodic. The original proof is due to Bose and Madan. 相似文献
15.
Miyuki Yamada 《Semigroup Forum》1971,2(1):154-161
In the previous paper [6], it has been proved that a semigroup S is strictly regular if and only if S is isomorphic to a quasi-direct
product EX Λ of a band E and an inverse semigroup Λ. The main purpose of this paper is to present the following results and some relevant
matters:
(1) A quasi-direct product EX Λ of a band E and an inverse semigroup Λ is simple [bisimple] if and only if Λ is simple [bisimple], and (2) in case where
EX Λ has a zero element, EX Λ is O-simple [O-bisimple] if and only if Λ is O-simple [O-bisimple]. Any notation and terminology should be referred to
[1], [5] and [6], unless otherwise stated. 相似文献
16.
It is well-known that for a lattice-finite order Λ over a complete discrete valuation domain, the radical of Λ-lat (the category of Λ-lattices) is nilpotent modulo projectives. Iyama has shown that this property merely depends on the combinatorial
data given by the Auslander–Reiten quiver of Λ. Moreover, he established a criterion for a finite (symmetrizable) translation
quiver Q to be the Auslander–Reiten quivers of an order Λ. We improve his characterization by showing that the remaining conditions
on Q can be replaced by the existence of an additive function on the vertices of Q (Theorem 4). Our proof rests on a functorial theory of ladders, expressing the Auslander–Reiten structure of Λ-lat by means of an adjoint pair of functors L⊣L− in the homotopy category of two-termed complexes over Λ-lat.
Presented by I. Reiten
Mathematics Subject Classifications (2000) Primary: 16G70, 16G30; secondary: 16G60. 相似文献
17.
Miyuki Koiso 《manuscripta mathematica》1995,87(1):311-325
We generalize the classical Steiner symmetrization to surfaces with self-intersections. Then we apply the generalized Steiner
symmetrization to several isoperimetric problems. For example, let Г⊂ℝ3 be an analytic plane Jordan curve which is symmetric with respect to a plane ϖ (ϖ⊅Г). LetS be a compact immersed surface bounded by Λ which has the smallest area among all compact surfaces bounded by Λ with a fixed
volume. In this situation, under some additional assumptions, the wholeS is proved to be symmetric with respect to ϖ. When Λ is a round circle,S is proved to be a spherical cap or the flat disk bounded by Λ without any additional assumptions.
Dedicated to Professor Hideki Ozeki on his 60th birthday
This article was processed by the author using the Springer-Verlag TEX P Jourlg macro package 1991. 相似文献
18.
S. Shkarin 《Integral Equations and Operator Theory》2009,64(1):115-136
It is shown that if 1 < p < ∞ and X is a subspace or a quotient of an ℓp-direct sum of finite dimensional Banach spaces, then for any compact operator T on X such that ∥I + T∥ > 1, the operator I + T attains its norm. A reflexive Banach space X and a bounded rank one operator T on X are constructed such that ∥I + T∥ > 1 and I + T does not attain its norm.
The author would like to thank E. Shargorodsky for his interest and comments. 相似文献
19.
We introduce new classes of sets called Λ
g
-closed sets and Λ
g
-open sets in topological spaces. We also investigate several properties of such sets. It turns out that Λ
g
-closed sets and Λ
g
-open sets are weaker forms of closed sets and open sets, respectively and stronger forms of g-closed sets and g-open sets, respectively.
Dedicated to Professor Maximilian Ganster on the occasion of his 50th birthday 相似文献
20.
An algebra A over a field k is FCR if every finite dimensional representation of A is completely reducible and the intersection of the kernels of these representations is zero. We give a useful characterization
of FCR-algebras and apply this to C
*-algebras and to localizations. Moreover, we show that “small” products and sums of FCR-algebras are again FCR.
Received: 25 October 2000 相似文献