Holomorphic Functions of Exponential Growth on Abelian Coverings of a Projective Manifold

Let M be a projective manifold, p: M _G M a regular covering over M with a free Abelian transformation group G. We describe the holomorphic functions on M _G of an exponential growth with respect to the distance defined by a metric pulled back from M. As a corollary, we obtain Cartwright and Liouville-type theorems for such functions. Our approach brings together the L ₂ cohomology technique for holomorphic vector bundles on complete Kähler manifolds and the geometric properties of projective manifolds.     

Gorenstein Injective and Projective Complexes with Respect to a Semidualizing Module

Let R be a commutative (possibly non-Noetherian) ring (in order to make things less technical) and C a semidualizing R-module. In this article, we introduce and investigate the notion of G _C -injective (G _C -projective) complexes. This extends Enochs and García Rozas's notion of Gorenstein injective (Gorenstein projective) complexes. We then show that a complex X is G _C -injective (G _C -projective) if and only if X ^m is a G _C -injective (G _C -projective) module for each m ∈ ?.     

t-Extending Modules and t-Baer Modules

We introduce the notions of “t-extending modules,” and “t-Baer modules,” which are generalizations of extending modules. The second notion is also a generalization of nonsingular Baer modules. We show that a homomorphic image (hence a direct summand) of a t-extending module and a direct summand of a t-Baer module inherits the property. It is shown that a module M is t-extending if and only if M is t-Baer and t-cononsingular. The rings for which every free right module is t-extending are called right Σ-t-extending. The class of right Σ-t-extending rings properly contains the class of right Σ-extending rings. Among other equivalent conditions for such rings, it is shown that a ring R is right Σ-t-extending, if and only if, every right R-module is t-extending, if and only if, every right R-module is t-Baer, if and only if, every nonsingular right R-module is projective. Moreover, it is proved that for a ring R, every free right R-module is t-Baer if and only if Z ₂(R _R ) is a direct summand of R and every submodule of a direct product of nonsingular projective R-modules is projective.     

Complemented copies of ℓ<Subscript>p</Subscript> spaces in tensor products

We give sufficient conditions on Banach spaces X and Y so that their projective tensor product X ⊗_π Y, their injective tensor product X ⊗_ɛ Y, or the dual (X ⊗_π Y)^* contain complemented copies of ℓ_p.     

Auslander Class,G C,and C–projective Modules Modulo Exact Zero-divisors

For a semidualizing module C over a ring R, we study the following classes modulo exact zero divisors: G _C –projectives, 𝒢 _C ; the Auslander class 𝒜 _C ; the Bass class ? _C ; 𝒫 _C –projective; ? _C –projective; and ? _C –injective dimensions.     

Two Commuting Involutions Fixing RP1(2m + 1) S RP2(2m + 1)*

Let Z₂ denote a cyclic group of 2 order and Z₂² = Z₂ ×Z₂ the direct product of groups. Suppose that (M, Φ) is a closed and smooth manifold M with a smooth Z₂² -action whose fixed point set is the disjoint union of two real projective spaces with the same dimension. In this paper, the authors give a sufficient condition on the fixed data of the action for (M, Φ) bounding equivariantly.     

NIL PROBLEMS REVISITED FOR ALMOST NILPOTENT RINGS

Abstract

We begin with the notion of K-flat projectivity. For each biframe L we then introduce a binary relation ?L on it. The K-flat projective biframes are exactly such biframes with each element a of the total (first, second) part approximated by the elements x of the total (first, second) part, x?_L a and the relation ?_L being stable wrt. the meet operation on L. Further on, we introduce the notion of a K-comonad and characterize K-flat projective biframes as those biframes having a coalgebra structure for the K-comonad. The K-coherent biframes and K-flat projective biframes are coreflective in all biframes.     

Rational Surfaces with Many Nodes

We describe smooth rational projective algebraic surfaces over an algebraically closed field of characteristic different from 2 which contain n b ₂ –2 disjoint smooth rational curves with self-intersection –2, where b ₂ is the second Betti number. In the last section this is applied to the study of minimal complex surfaces of general type with p _g = 0 and K² = 8, 9 which admit an automorphism of order 2.     

Realization of primitive branched coverings over closed surfaces following the hurwitz approach

Let V be a closed surface, H⊑π₁(V) a subgroup of finite index l and D=[A ₁,...,A _m ] a collection of partitions of a given number d≥2 with positive defect v(D). When does there exist a connected branched covering f:W→V of order d with branch data D and f∶W→V It has been shown by geometric arguments [4] that, for l=1 and a surface V different from the sphere and the projective plane, the corresponding branched covering exists (the data D is realizable) if and only if the data D fulfills the Hurwitz congruence v(D)э0 mod 2. In the case l>1, the corresponding branched covering exists if and only if v(D)э0 mod 2, the number d/l is an integer, and each partition A _i ∈D splits into the union of l partitions of the number d/l. Here we give a purely algebraic proof of this result following the approach of Hurwitz [11]. The realization problem for the projective plane and l=1 has been solved in [7,8]. The case of the sphere is treated in [1, 2, 12, 7].     

Hyperspaces of nowhere topologically complete spaces

It is proved that ifX is a connected locally continuumwise connected coanalytic nowhere topologically complete space, then the hyperspace 2 ^X of all nonempty compact subsets ofX is strongly universal in the class of all coanalytic spaces. Moreover, 2 ^X is homeomorphic to Π₂ ifX is a Baire space, and toQ∖Π₁ ifX contains a dense absoluteG _δ-setG ⊂X such that the intersectionG ∩U is connected for any open connectedU ⊂X. (Here Π₁, Π₁⊂X are the standard subsets of the Hilbert cubeQ absorbing for the classes of analytic and coanalytic spaces, respectively.) Similar results are obtained for higher projective classes. Translated fromMatematicheskie Zametki, Vol. 62, No. 1, pp. 35–51, July, 1997. Translated by O. V. Sipacheva     

When Some Complement of a Submodule Is a Summand

A module M is said to satisfy the C ₁₁ condition if every submodule of M has a (i.e., at least one) complement which is a direct summand. It is known that the C ₁ condition implies the C ₁₁ condition and that the class of C ₁₁-modules is closed under direct sums but not under direct summands. We show that if M = M ₁ ⊕ M ₂, where M has C ₁₁ and M ₁ is a fully invariant submodule of M, then both M ₁ and M ₂ are C ₁₁-modules. Moreover, the C ₁₁ condition is shown to be closed under formation of the ring of column finite matrices of size Γ, the ring of m-by-m upper triangular matrices and right essential overrings. For a module M, we also show that all essential extensions of M satisfying C ₁₁ are essential extensions of C ₁₁-modules constructed from M and certain subsets of idempotent elements of the ring of endomorphisms of the injective hull of M. Finally, we prove that if M is a C ₁₁-module, then so is its rational hull. Examples are provided to illustrate and delimit the theory.     

Preparation, structure, magnetic properties and special magnetoresistance effect of Lao.67Sr0.33Mn03+δ/Pr0.7Cao.3 Mn03+δ/Lao.67Sro.33Mn03+δ trilayered thin films

The La_0,67Sr_0.33Mn0_{3 +δ}/Pr_0.7Ca_o.3Mn0_3+δ/La_0.67Sr_0.33Mn0_3+δ(LPL) trilayered films on (100)LaA-1O₃ substrates are prepared by using direct current (DC) magnetron sputtering method. The results obtained by means of X-ray powder diffractometer show that all films are the high quality epitaxial films. The results gained by SQUID magnetometer indicate that there is a magnetic coupling in the LPL trilayered films. The resistivities of LSMO, PC-MO and LPL films are measured using standard four-probe method and analyzed log_p-1/T curve. From the results it is concluded that the middle-layered PCMO which is ferromagnetic may play a role of intra-magnetic field, which weakens the paramagnetism of LSMO film, lowersp _max and enlargesT _p which is the transition temperature from metal to insulator, just as the applied magnetic field does. And the middle-layered PCMO may induce the change of the density of states in the LSMO’s gap. The two reasons above make the resistivity andT _p of the samples in zero field change with the thickness of PCMO layers. Project supported by the Chinese Academy of Sciences and the Foundation of State Science and Technology Commission of China.     

On Relative K 2-Group of Split Radical Ideals

Let I be a split radical ideal of a ring R. In this article, the exact sequence 1 → K ₂(R, I) → U _R (I) → V(R, I) → 1 is given by using the method of extension of groups, where U _R (I) is determined by generators and relations. The results of Maazen and Stienstra on the presentation for relative K ₂ group of split radical pairs are extended and amplified.     

Modules Whose t-Closed Submodules Have a Summand as a Complement

We define and investigate T ₁₁-type modules as a generalization of t-extending modules, and modules satisfying C ₁₁ condition. A module M is said to be T ₁₁-type if every t-closed submodule of M has a complement which is a direct summand. Direct sums of T ₁₁-type modules inherit the property. Some equivalent conditions for a module M to be T ₁₁-type are given. We characterize a module M for which every direct summand satisfies T ₁₁ condition. If R _R is T ₁₁-type, then R/Z ₂(R _R ) is a C ₂ ring if and only if it is a von Neumann regular ring. Applying this result, we characterize a right t-extending (resp., finitely Σ-t-extending, or Σ-t-extending) ring R for which R/Z ₂(R _R ) is von Neumann regular.     

Combinatorial generalizations of generalized quadrangles of order (2, 2)

We study substructures of a projective space PG(n, 2) represented in terms of elementary combinatorics of finite sets, which generalize the Sylvester’s representation of the generalized quadrangle of order (2, 2). Their synthetic properties are established and automorphisms are characterized.      

Construction of Ternary H v -groups and Ternary P-hyperoperations

In this paper, we study the concept of ternary H _v -groups and some their properties. We give some examples of ternary H _v -groups. Also, we consider the fundamental relation β* on a ternary H _v -group and prove that β* is a compatible relation on a ternary H _v -group. In addition, we define the P-hyperoperation, and then, we construct a new ternary H _v -group.     

态R_0代数

本文研究了R_0代数上有关态算子的问题.利用MV-代数上内态的引入方法引入了态算子,定义了态R_0代数,它是R_0代数的一般化.给出了一些非平凡态R_0代数的例子并讨论了态R_0代数的一些基本性质.在此基础上给出了态滤子和态局部R_0代数的概念,并利用态滤子刻画了态局部R_0代数.推广了局部R_0代数的相关理论.     

Configuration Spaces of Points on the Circle and Hyperbolic Dehn Fillings, II (Dedicated to Professor Mitsuyoshi Kato on his 60th birthday)/atl>

In our previous paper (Topology 38 (1999), 497–516), we discussed the hyperbolization of the configuration space of n ( 5) marked points with weights in the projective line up to projective transformations. A variation of the weights induces a deformation. It was shown that this correspondence of the set of the weights to the Teichmüller space when n = 5 and to the Dehn filling space when n = 6 is locally one-to-one near the equal weight. In this paper, we establish its global injectivity.     

Comparison of 3-Dimensional ℤ-Graded and ℤ2-Graded L ∞ Algebras

This article explores L _∞ structures on 3-dimensional vector spaces with both ?- and ?₂-gradings. Since ?-graded L _∞ algebras are special cases of ?₂-graded algebras in the induced ?₂-grading, there are generally fewer ?-graded L _∞ structures on a given space. However, degree zero automorphisms (rather than even automorphisms) determine equivalence in a ?-graded space. We therefore find nontrivial examples in which the map from the ?-graded moduli space to the ?₂-graded moduli space is bijective, injective but not surjective, or surjective but not injective. Additionally, we study how the codifferentials in the moduli spaces deform into other nonequivalent codifferentials.