幂群与序关系

设Ｇ为非ｍｏｎｏｉｄａｌ群，Ｅ是它的正规子集，满足Ｅ²＝Ｅ并且１_Ｇ∈／Ｅ．利用Ｅ作为正锥，可以在Ｇ上定义一个偏序，并且Ｇ成为一个偏序群．这样就可以利用这个序关系同时研究群Ｇ以及Ｇ上的以Ｅ为单位元的幂群．当Ｅ是极大子半群时，得到Ｇ的一个结构定理；在Ｇ是格序群的条件下，Ｇ上的幂群Γ可以膨胀为一个拟商群．     

包含紧算子理想的Toeplitz算子代数的刻画

设G为一个torsion-free的离散群,（G,G＋）为一个拟序群,记T^G (G)为相应的Toeplitz算子代数,K(l^2(G 1)为l^2(G )上的紧算子全体,本文证明了K(l^2(G ))增包含于T^G (G)当且仅当下列两个条件时满足。（1）（G,G＋）为一个序群,（2）G中存在一个最小的正元。     

拟偏序群上的Toeplitz算子

本文研究拟偏序群上的Toeplitz算子     

量化Domain理论的L-Fuzzy式处理(Ⅱ)L-Fuzzy拟序集的表示

本文是文献的续。对于固定的Frame L，本文证明了每个LF-拟序集可以等价地表示为拟序的层，该结果与L-Fuzzy集的分解和表示定理类似。由这此定理可得出以下结论：一类量化Domain(例如，广义超度量Domain)实际上是将满足一定条件的拟序族进行“粘贴”的结果(按照层论的语言叙述，就是拟序的层)，而通常的拟序则是常值拟序层的特例。     

偏序半群的偏序扩张

引入了偏序半群(S,·,≤)上的半拟序σ及模σ半拟链的概念.通过模σ半拟链,将S的偏序≤扩张为≤*,讨论了(S,*,≤*)是偏序半群的充分条件,并获得了若干理想的结果.特别地,得到了SPO(S)到PO(S)的两个半格同态定理.最后,还给出了S的满足某些给定条件的有限子集在≤*下成链的充要条件.     

量化Domain理论的L-Fuzzy式处理(II) L-Fuzzy拟序集的表示

本文是文献[4]的续。对于固定的FrameL,本文证明了每个LF-拟序集可以等价地表示为拟序的层,该结果与L-Fuzzy集的分解和表示定理类似。由这此定理可得出以下结论:一类量化Domain(例如,广义超度量Domain)实际上是将满足一定条件的拟序族进行"粘贴"的结果(按照层论的语言叙述,就是拟序的层),而通常的拟序则是常值拟序层的特例。     

群的形变收缩及Toeplitz代数

设G为一个离散群,(G,G_ )为一个拟偏序群使得G_ ~0=G_ ∩G_ ~(-1)为G的非平凡子群。令[G]为G关于G_ ~0的左倍集全体,|G_ |为[G]的正部。记T~(G_ )和T~([G_ ])为相应的Toeplitz代数。当存在一个从G到G_ ~0上的形变收缩映照时,我们证明了T~(G_ )酉同构于T~([G_ ])×C_r~*(G_ ~0)的一个C_-~*c子代数。若进一步,G_ ~0还为G的一个正规子群,则T~(G_ )与T~([G_ ])×C_r~*(G_ ~0)酉同构。     

拟序下非连续增算子新的广义不动点定理

运用序方法研究了拟序空间X中具A=CB型非连续增算子的广义不动点的存在性问题,证明了在拟序空间X中具A=CB型非连续增算子存在最小广义不动点和最大广义不动点.所得结果推广了相关结论.     

6字0—1码借助8×8阵的编码变换

本文就6字0-1码同序8&;#215;8阵的运动群以及此阵的更序群揭示6字0-1码的编码变换。     

双生成元$A_n$型拟遗传代数的拟遗传序

本文讨论双生成元$A_n$型代数的拟遗传序的性质,给出了该类代数的单模序是拟遗传序的充分必要条件,并利用组合技巧得出了该类代数拟遗传序的数目.     

Lexicographic Products of Half Linearly Ordered Groups

The notion of the half linearly ordered group (and, more generally, of the half lattice ordered group) was introduced by Giraudet and Lucas [2]. In the present paper we define the lexicographic product of half linearly ordered groups. This definition includes as a particular case the lexicographic product of linearly ordered groups. We investigate the problem of the existence of isomorphic refinements of two lexicographic product decompositions of a half linearly ordered group. The analogous problem for linearly ordered groups was dealt with by Maltsev [5]; his result was generalized by Fuchs [1] and the author [3]. The isomorphic refinements of small direct product decompositions of half lattice ordered groups were studied in [4].     

Strong Projectability of Lattice Ordered Groups

In this paper we prove that the lateral completion of a projectable lattice ordered group is strongly projectable. Further, we deal with some properties of Specker lattice ordered groups which are related to lateral completeness and strong projectability. This work was supported by VEGA grant 2/1131/21.     

Distinguished Completion of a Direct Product of Lattice Ordered Groups

The distinguished completion E(G) of a lattice ordered group G was investigated by Ball [1], [2], [3]. An analogous notion for MV-algebras was dealt with by the author [7]. In the present paper we prove that if a lattice ordered group G is a direct product of lattice ordered groups G _i (i I), then E(G) is a direct product of the lattice ordered groups E(G _i). From this we obtain a generalization of a result of Ball [3].     

Toeplitz algebras on discrete abelian quasily ordered groups

In this note, Toeplitz operators on discrete abelian quasily ordered groups are studied, and a theorem of R. Douglas is generalized.

     

Affine completeness and wreath product decompositions of lattice ordered group

Let Δ and H be a nonzero abelian linearly ordered group or a nonzero abelian lattice ordered group, respectively. In this paper we prove that the wreath product of Δ and H fails to be affine complete. Supported by VEGA grant 2/4134/24. This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence-Physics of Information, grant I/2/2005.     

Extensions of lattice-ordered groups

A number of conditions are specified which are sufficient for totally ordered groups with polycyclic factor group to contain a finite normal series of convex subgroups whose factors possess good enough properties. In any case studying such totally ordered groups is reduced to treating extensions of these groups as well as their virtually o-equivalent extensions. The concept of a virtually o-equivalent extension is a particular case of the notion of an Archimedean extension. Supported by RFBR project No. 03-01-00320. Translated from Algebra i Logika, Vol. 47, No. 5, pp. 529–540, September–October, 2008.     

O-2-transitive automorphism groups with abelian stabilizer of a point

It is proved that an o-2-transitive group of order automorphisms of a totally ordered set with Abelian stabilizer of a point is the permutation groupF={φ(a, b)‖a, bεP, a>0, (x)φ(a, b)=xa+b forxεP} of a totally ordered fieldP. Translated fromMatematicheskie Zametki, Vol. 65, No. 2, pp. 289–293, February, 1999.     

关于格序群的极大素子群

研究了格序群的极大素子群的性质以及由素子群根系确定的几种格序群类的结构。     

On the Affine Completeness of Lattice Ordered Groups

In the paper it is proved that a nontrivial direct product of lattice ordered groups is never affine complete.     

可换全序群的极大上下对

ＬｅｔＧｂｅａｎａｂｅｌｉａｎｏ ｇｒｏｕｐ (ｓｅｅ[1 ] )ｔｈｒｏｕｇｈｏｕｔａｎｄａ ,ｂ∈Ｇ .Ｉｆａ =0ｏｒ ｂ ａ ,ｔｈｅｎｗｅｓａｙｔｈａｔａｌｉｅｓａｂｏｖｅｂｏｒｂｌｉｅｓｂｅｌｏｗａ .ＬｅｔＡ ,ＢｂｅｔｗｏｓｕｂｇｒｏｕｐｓｏｆＧ .ＩｆｅａｃｈｅｌｅｍｅｎｔｏｆＡｌｉｅｓａｂｏｖｅａｌｌｅｌｅｍｅｎｔｓｏｆＢ ,ｔｈｅｎｗｅｓａｙｔｈａｔＡｌｉｅｓａｂｏｖｅＢｏｒＢｌｉｅｓｂｅｌｏｗＡ .ＩｆＡｉｓｍａｘｉｍａｌａｍｏｎｇｔｈｏｓｅｓｕｂｇｒｏｕｐｓｔｈａｔｌｉｅａｂｏｖｅＢ ,ｔｈｅｎｗｅ…