适合无限维实零点定理的序域之结构Ⅰ

本文的目的是建立适合无限维实零点定理的序域的结构定理．作为预备工作,文章的第一部分研究一类无秩为d的裂缝的序群,这里d是无限基数．藉助于Hahn嵌入定理,本文给出了无秩为d的裂缝的序群的结构．     

适合无限维实零点定理的序域之结构Ⅱ

在本文的第二部分中,我们研究了适合无限维实零点定理的序域的结构．通过嵌入,我们证明了,一个序域适合无限维实零点定理,当且仅当它的实闭包同构于域的某个具有无限维逼近性质的子域,这里是一个无裂缝的可除序群,｛Γ｝是指数在中,系数为实数的形式幂级数域．     

适合无限维实零点定理的序域之结构II

在本文的第二部分中,我们研究了适合无限维实零点定理的序域的结构。通过嵌入,我们证明了,一个序域适合无限维实零点定理,当且仅当它的实闭包同构于域Ｒ｛Γ｝的某个具有无限维逼近性质的子域。这里Γ是一个无裂缝的可除序群,Ｒ｛Γ｝是指数在Γ中,系数为实数的形式幂级数域。     

无限维空间中的实零点定理

在本文中，我们建立了无限维空间中的实零点定理，同时从仿射空间的拓扑结构和域的序结构两个方面，分别刻划了适合无限维实零点定理的序域．此外，本文有例子表明，对任意的基数α，确实存在适合α维实零点定理的序域．     

两类整环上的上三角矩阵群(Ⅰ)

本文从两类整环上的二阶上三角矩阵入手,构造了两个3元生成的亚Abel群,给出了它们的清晰结构,研究了它们的剩余有限性质:一,证明了其中一个无限秩的亚Abel群是剩余有限p-群,这里p是任意素数.二,证明了另一个有限秩的亚Abel群没有这种整齐的剩余有限性质,尽管其结构要简单得多.本文的结果表明,无限可解群里秩的有限性条件对群的剩余有限性具有很大的影响.如何把本文的研究推广到高阶矩阵群,是值得进一步探索的问题.     

关于LIH KO-WEI猜想的证明

ＬｉｎＫｏ－Ｗｅｉ［１］提出猜想：如果Ｆ是由Ｂｎ中固定秩的不同元素生成的序理想,那么Ｆ是Ｓｐｅｒｎｅｒ系［１］,黄国泰就Ｆ是由Ｘ的子集Ｙ的所有相同秩的元素生成的序理想,证实了上述猜想［２］,本文完全证明了该猜想．本文使用的概念,符号见［２］．定理设ａ...     

有限秩的可解群的一个幂零条件

设 Ｇ是个有限秩的可解群,如果对无限多个素数ｐ, Ｇ是个剩余有限ｐ－群,那么 Ｇ是个有限秩的无挠幂零群．     

Frattini子群是无限循环群的有限生成幂零群

完整地确定了Frattini子群是无限循环群的有限生成幂零群的结构,证明了下面的定理.设G是有限生成幂零群,则G的Frattini子群是无限循环群当且仅当G可以分解为G=S×F×T,其中F是秩为s的自由Abel群,T=Z_m_1⊕Zm_2⊕…⊕Z_m_u,m_1,m_2,…,m_u都是大于1的没有平方因子的自然数,m_1|m_2|…|m_u,■式中d_1,d_2,…,d_r都是正整数,d_1|d_2|…|d_r.进一步,(d_1,d2,…,d_r;s;m_1…,m_2,…,m_u)是群G的同构不变量,即若群H也是Frattini子群是无限循环群的有限生成幂零群,那么G同构于H的充要条件是它们有相同的不变量.     

探讨有限莫利秩的域的结构和性质

环具有加法群和乘法群的二元代数运算结构,利用有限莫利秩的群的性质具有降链条件,与在无限域上的代数扩张的伽罗瓦理论结合,来研究有限莫利秩的无限域的结构和性质,主要成果为:有限莫利秩的无限域K,任意a∈K,整数n>0,方程xⁿ=a在域K中有解;假设域K是有限莫利秩的无限域,那么域K一定是代数闭域.     

无限亚局部循环群及其自同构群

作为之前工作的继续, 本文研究了无限亚局部循环群的结构以及它们的自同构和自同构群. 设 A,B 分别是秩1 的无挠Abel 群, G 为n 阶循环群. 群E 是A 被G 的扩张, G 被A 的扩张或者A 被 B 的扩张. 讨论了群E 的结构以及它们的自同构, 并得到了它们的自同构群.     

On a type of distributivity of lattice ordered groups

Let m be an infinite cardinal. Inspired by a result of Sikorski on m-representability of Boolean algebras, we introduce the notion of r _m-distributive lattice ordered group. We prove that the collection of all such lattice ordered groups is a radical class. Using the mentioned notion, we define and investigate a homogeneity condition for lattice ordered groups.     

Groups in which every subgroup of infinite rank is almost permutable

In this paper, the structure of locally finite groups of infinite rank whose subgroups of infinite rank are permutable in a subgroup of finite index is investigated.     

On dilworth’s theorem in the in finite case

The following theorem is proved: Letc be an infinite cardinal. There exists a partially ordered set of cardinalc, which contains no infinite independent subset, and which is not decomposable into less thanc chains.     

Critical exponent and critical blow-up for quasilinear parabolic equations

B ₂-groups are special (torsion-free) abelian Butler groups. The interest in this class of groups comes from representation theory. A particular functor, also called Butler functor, connects algebraic properties of the category of free abelian groups with (a few) distinguished subgroups with these Butler groups. This helps to understand Butler groups and caused lots of activities on Butler groups. Butler groups were originally defined for finite rank, however a homological connection discovered by Bican and Salce opened the investigation of Butler groups of infinite rank. Despite the fact that classifications of Butler groups are possible under restriction even for infinite rank (see a forthcoming paper by Files and Göbel [Mathematische Zeitschrift]), general structure theorems are impossible. This is supported by the following very special case of the Main Theorem of this paper, showing that any ring with a free additive group is an endomorphism ring of a Butler group. The result implies the existence of large indecomposable or of large superdecomposable Butler groups as well as the existence of counter-examples for Kaplansky’s test problems.     

On Some Interpolation Rules for Lattice Ordered Groups

Let be an infinite cardinal. In this paper we define an interpolation rule IR() for lattice ordered groups. We denote by C() the class of all lattice ordered groups satisfying IR(), and prove that C() is a radical class.     

There exist subdirectly irreducible commutative basic algebras of an arbitrary infinite cardinality which are not MV-algebras

It was recently proved by P. Wojciechowski that for any infinite cardinal there exists a linearly ordered MV-algebra of this cardinality. Since basic algebras are a (non-associative) generalization of MV-algebras, there rises a natural question if this is true also for basic algebras which are not MV-algebras. Using the construction by P. Wojciechowski and the modified construction by the first author, we can set up certain defectors which enable us to prove the result of the title.     

Finitely Generated Nilpotent Groups of Infinite Cyclic Commutator Subgroups

The aim of this paper is to determine the structure and to establish the isomorphic invariant of the finitely generated nilpotent group G of infinite cyclic commutator subgroup. Using the structure and invariant of the group which is the central extension of a cyclic group by a free abelian group of finite rank of infinite cyclic center, we provide a decomposition of G as the product of a generalized extraspecial Z-group and its center. By using techniques of lifting isomorphisms of abelian groups and equivalent normal form of the generalized extraspecial Z-groups, we finally obtain the structure and invariants of the group G.