Abelian范畴中的Jordan-H(o)lder定理

利用Abdian范畴中子对象的交与并的性质，将模范畴中的蝴蝶结引理推广到Abelian范畴中，并据此证明了Abelian范畴中的Jordan-Holder定理．     

拉回正合范畴中小子对象的探讨

拉回正合范畴是Abelian范畴的真正推广,是界在正合范畴与Abelian范畴之间的一类范畴.本文利用拉回-推出,引进拉回正合范畴的小子对象概念,并给出小子对象相关的性质以及等价条件.     

拟Abelian范畴上函子范畴的局部化

通过拟Abelian范畴的局部类构造出函子范畴的局部类,进一步研究函子范畴的局部化范畴与局部化范畴的函子范畴之间的关系.     

一类Hamiltion系统的Abel积分的零点个数估计

In this paper, we discuss the estimation of the number of zeros of the Abelian integral for the quadratic system which has a periodic region with a parabola and a straight line as its boundary when we perturb the system inside the class of all polynomial systems of degree n. The main result is that the upper bound for the number of zeros of the Abelian integral associated to this system is 3n-1.     

拟-赋范 Abel 群的实内插方法的几个问题

将赋范向量空间的实内插方法推广到拟-赋范Abelian群上去,所得到的结果在[1]及[5]中有所论述。应该指出的是后一种情形不但以c-三角不等式代替通常的三角不等式,而且对参数q的适应范围也有进一步扩充,这就必须对原来的定义及其有关结果的证明给以必要的不同于前者的论述。本文就是为了适应这种需要,在拟-赋范Abelian群上对[1]～[4]中的结果加以研究和讨论,并给出其相应的结果和必要的证明。     

关于弱半可根群

In this paper, we prove that if a torsion nilpotent group G is a weak semi-radicable group, then every Sylow p-group Gp is a central-by-finite p-group, and moreover Gp's center ζ(GP) satisfies |ζ(GP) : (ζ(GP))P| <∞, that is, ζ(GP) = D×F, where D is a divisible Abelian group, and F is a finite Abelian group.     

一类可积非哈密顿系统的极限环个数的上界

In this paper, we consider the perturbations of two non-Hamiltonian integrable systems(1.3)μ, (4.1)μ. For the former,it is proved that the system under the polynomial perturbations hasat most f-n/2] limit cycles in the finite plane and the upper bound is sharp. The proof relies on acareful analysis of a related Abelian integral. For the latter, we obtain an estimate number of isolatedzeros of the corresponding Abelian integral.     

群中的一个组合问题

设 G 是一个有限 Abelian 群,c(G)是最小正整数使得 G 的任一合于|S|(?)c(G),0(?)S 的子集 S 均有性质:G 的每一个元均可表为 S 的某些元之和.本文确定了一大类 Abelian 群 G 相应的 c(G).对大部分有限交换 P-群 G,c(G)已由本文确定.     

边增加常返构型改变（英文）

研究图上Abelian沙堆模型的常返构型问题.刻画了当图的边增加时,图的常返构型如何改变.     

关于加法范畴上的两个猜测

本文继文［１］在加法范畴上引进左Ｚｏｒｎ条件、Ｋ－商范畴等概念，讨论范畴上的Ｋｏｔｈｅ猜测与Ｈｅｒｅｔｅｉｎ猜测，得到两个猜测成立的充要条件，并同时得到环论上的一个新结果和两个猜测成立的条件．这个条件改进了文［３］中的条件．     

A study of cofiniteness through minimal associated primes

In this article, we shall investigate the concepts of cofiniteness of local cohomology modules and Abelian categories of cofinite modules over arbitrary Noetherian rings. Then we shall improve some of the well known results in the area.     

Projective and injective objects of the categories dual to \mathfrak{A}\mathfrak{B}

The categories dual to the category of Abelian groups (including the category of compact Abelian groups) are considered. In these categories, structure theorems on injective and projective objects are proved, and some projective coverings are calculated. In the category of compact Abelian groups, the notion of connected hull is introduced; some results on connected hulls are obtained and examples are given. Bibliography: 7 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 321, 2005, pp. 168–182.     

Lefschetz Motives and the Tate Conjecture

A Lefschetz class on a smooth projective variety is an element of the Q-algebra generated by divisor classes. We show that it is possible to define Q-linear Tannakian categories of abelian motives using the Lefschetz classes as correspondences, and we compute the fundamental groups of the categories. As an application, we prove that the Hodge conjecture for complex abelian varieties of CM-type implies the Tate conjecture for all Abelian varieties over finite fields, thereby reducing the latter to a problem in complex analysis.     

Idempotent functors and localizations in categories of modules and Abelian groups

The present paper contains various results on idempotent functors and localizations in categories of modules and Abelian groups.     

Reconstruction of a Variety from the Derived Category and Groups of Autoequivalences

We consider smooth algebraic varieties with ample either canonical or anticanonical sheaf. We prove that such a variety is uniquely determined by its derived category of coherent sheaves. We also calculate the group of exact autoequivalences for these categories. The technics of ample sequences in Abelian categories is used.     

Semicorings and Semicomodules

In this paper, we introduce and investigate semicorings over associative semirings and their categories of semicomodules. Our results generalize old and recent ones on corings over rings and their categories of comodules. The generalization is not straightforward and even subtle at several places due to the nature of the base category of commutative monoids which is neither Abelian (not even additive) nor homological, and has no nonzero injective objects. To overcome these and other difficulties, a combination of methods and techniques from categorical, homological and universal algebra is used including a new notion of exact sequences of semimodules over semirings.     

An Embedding Theorem for Abelian Monoidal Categories

We show that, with some technical conditions, an Abelian monoidal category admits a monoidal embedding into the category of bimodules over a ring. The case of semisimple rigid monoidal categories is studied in more detail.     

Transfinite Diameter with Respect to the Neumann Function

In this paper, we study holomorphically isomorphic Abelian groups, i.e., Abelian groups with isomorphic holomorphs. We also study a generalization of the concept of holomorphic isomorphism, namely, almost holomorphic isomorphism, which is deeply connected with normal Abelian subgroups of holomorphs of Abelian groups. Torsion-free Abelian groups that are determined by their holomorphs are highlighted from different classes. In particular, it has been found that any homogeneous separable group can be determined by its holomorph in the class of all Abelian groups.     

Weakly Linearly Compact Topological Abelian Groups

In this paper, we study linearly topological groups. We introduce the notion of a weakly linearly compact group, which generalizes the notion of a weakly separable group, and examine the main properties of such groups. For weakly linearly compact groups, we construct the character theory and present an algebraic characterization of some classes of such groups. Some well-known theorems for periodic Abelian groups are generalized for the case of linearly discrete, topological Abelian groups; for linearly compact and linearly discrete topological Abelian groups, we also construct the character theory and study some important properties of linearly discrete groups. For linearly discrete, topological Abelian groups, we analyze the splittability condition (Theorem 3.12) and present the characteristic condition of decomposability of a discrete group G into the direct sum of rank-1 groups. We also present an algebraic characterization of linearly compact groups. We introduce the notion of a weakly linearly compact, topological Abelian group, which generalizes the notion of a weakly separable Abelian group, and examine some properties of such groups. These groups are a generalization of fibrous Abelian groups introduced by Vilenkin. We give an algebraic characterization of divisible, weakly locally compact Abelian groups that do not contain nonzero elements of finite order (Proposition 7.9). For weakly locally compact Abelian groups, we construct universal groups.