半完全环的K1群

在一定的条件下，半完全环R的K1群可以通过R／J（R）的直和分解得到。     

有限交换环上典型群的Sylow子群

令Ｒ为有限交换局部环，Ｍ表其唯一的极大理想，ｋ表其剩余类域．本文定出了Ｒ上的一般线性群ＧＬｎＲ，辛群Ｓｐ２ｎＲ及双曲正交群Ｏ２ｎＲ的Ｓｙｌｏｗ子群．一般讲，若ｃｈａｒｘ＝ｐ，上述三类典型群的Ｓｙｌｏｗ ｐ－子群分别同构于由某些特殊形式的矩阵生成的子群；若ｃｈａｒｋ≠ｐ，上述三类典型群的Ｓｙｌｏｗｐ－子群分别同构于一循环群或半二面体群与若干Ｚｐ型循环群的圈积。     

交换环上多项式结式的性质

本文主要讨论交换环上多项式结式的一些性质.首先,我们证明了交换环上一种乘积的结式等于结式的乘积的性质,然后,我们证明了交换环上一种和的结式具有的性质,并且给出了交换环上结式为零的一个充分条件.     

交换环上Rao正则矩阵的广义Cramer法则

Gong Z,Aldeen M和Elsner L在[A note on a generalized Cramer’s rule,Linear AlgebraApp.,2002,340:253-254]中给出结论:对任意的k,α∈Qk,n,β∈Qk,m有|Xα,β|=|A-1|AYαβ,其中A∈n×n可逆矩阵,AX=Y.本文给出交换环上Rao正则矩阵的广义Cramer法则.     

On Polynomial Functions over Finite Commutative Rings

Let R be an arbitrary finite commutative local ring. In this paper, we obtain a necessary and sufficient condition for a function over R to be a polynomial function. Before this paper, necessary and sufficient conditions for a function to be a polynomial function over some special finite commutative local rings were obtained.     

有限交换环上线性群的Carter子群

令Ｒ为有限交换局部环，Ｋ为其剩余类域．本文研究了Ｒ上一般线性群ＧＬｎＲ的Ｃａｒｔｅｒ子群的存在性及结构．得到的结果是：若ｃｈａｒＫ为奇数或Ｋ＝Ｆ２，ＧＬｎＲ中存在唯一的Ｃａｒｔｅｒ子群的共轭类，即Ｓｙｌｏｗ－２子群的正规化子；若ｃｈａｒＫ＝２且｜Ｋ｜＞２，ＧＬｎＲ中不含Ｃａｒｔｅｒ子群．     

有限交换环上典型群的Carter子群

令R为有限交换局部环,K为其剩余类域,令|K|=q.本文研究了R上辛群Sp2nR和正交群O2nR的Carter子群的存在性及结构,并给出R上正交群O2nR在q≡-1（mod 4）情况下的Sylow 2-子群的正确描述.     

有限交换环上极限线性群的Sylowp—子群

本文给出了有限交换局部环Ｒ上无限线性群ＧＬ（Ｒ）＝∪ｎＧＬｎＲ的Ｓｙｌｏｗｐ－子群的形式．令Ｍ是有限交换局部环Ｒ的唯一极大理想，ｋ＝Ｒ／Ｍ为Ｒ的剩余类域．用Ｘ（ｋ）表示ｋ的特征，并假定Ｐ与ｘ（ｋ）互素．作者证明了：ＧＬ（Ｒ）的任一Ｓｙｌｏｗｐ－子群Ｓ或者同构于的可数无限直积与Ｐ（ｊ）的无限直积的直积（当Ｐ≠２或Ｐ＝２，Ｘ（ｋ）β≡１（ｍｏｄ４））或者同构于Ｐｉ的无限直积与Ｐ（ｊ）的无限直积的直积（当Ｐ＝２，Ｘ（ｋ）β≡３（ｍｏｄ４）），这里，只是ＧＬ（ｅｐｉ）Ｒ（分别地，ＧＬ（２ｒｉ）Ｒ）的Ｓｙｌｏｗｐ－子群，Ｐ（ｊ））同构于Ｐ＝∪ｉ∈Ｉｐｉ，Ｉ是可数集．     

某些K_2O_F的结构(英文)

本文研究二次数域 Ｆ＝ 的 Ｋ２ＯＦ结构,其中 ｄ－３ ｍｏｄ ９和 ｄ ≠－３．找到了关于Ｆ＝的Ｋ２ＯＦ的３阶元和Ｆ＝的Ｋ２ＯＦ的生成元,推广Ｔ Ｂａｓｓ和 Ｔａｔｅ的一个定理和给出了 Ｆ＝ 的 Ｋ２ＯＦ的结构以及 ＳＬｎ（ＯＦ）（ｎ≥３）的表示关系．     

交换环上辛代数的导子代数(英文)

对含幺交换环上辛代数的导子代数做了详细的描述.     

交换环上辛代数的导子代数

对含幺交换环上辛代数的导子代数做了详细的描述.     

可换环上一些线性李代数的扩代数

设R是任意含单位元的可换环,gl(n,R)是R上n级一般线性李代数.t表示gl(n,R)中所有上三角矩阵组成的子代数,d表示gl(n,R)中所有对角矩阵组成的子代数.本文将分别确定t在gl(n,R)中的扩代数和d在t中的扩代数.     

The Zero Divisor Graphs of Commutative Local Rings of Order p 4 and p 5

To each commutative ring R we can associate a zero divisor graph whose vertices are the zero divisors of R and such that two vertices are adjacent if their product is zero. Detecting isomorphisms among zero divisor graphs can be reduced to the problem of computing the classes of R under a suitable semigroup congruence. Presently, we introduce a strategy for computing this quotient for local rings using knowledge about a generating set for the maximal ideal. As an example, we then compute Γ(R) for several classes of rings; with the results in [4 Bloomfield , N. , Wickham , C. ( 2010 ). Local rings with genus 2 zero divisor graph . Comm. Alg. 38 ( 8 ): 2965 – 2980 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]] these classes include all local rings of order p ⁴ and p ⁵ for prime p.     

The Structures of the Cohomology Rings of Wreathed 2-Groups

Let S be a wreathed 2-group. In this article we construct a free ?S-resolution of ? and describe the ring structure of the cohomology of wreathed 2-group S.     

可换幺半群的结构

关于“群”有各种各样的定义 ,本文给出了有限幺半群成为群的一个条件 .并对有限可换幺半群进行了讨论 ,通过对它的商集的研究 ,建立了有限可换幺半群与有限可换幺群之间的联系 ,从而揭示了有限可换幺半群的结构     

Nilpotent Elements and Idempotents in Commutative Group Rings #

Flatness properties of acts over monoids and their connection with monoid amalgamation have been investigated for almost four decades and a substantial literature on the subject has now appeared. Analogous research, concerning the action of partially ordered monoids on partially ordered sets and its relation to pomonoid amalgamation, was begun in 1980s in two articles by S. M. Fakhruddin. The subject then remained dormant until the recent past when several articles on flatness in the setting of ordered monoids acting on posets (briefly, S-posets) appeared. It has now been established that the introduction of order results in severe restrictions as far as absolute flatness is concerned. Also, after formulating in the ordered context the Representation Extension and Right Congruence Extension Properties, first used by T. E. Hall to study semigroup amalgams, the authors recently observed in their article [4 Bulman-Fleming , S. , Nasir , S. ( 2010 ). Examples concerning absolute flatness and amalgamation in pomonoids . Semigroup Forum 80 : 272 – 292 .[Crossref], [Web of Science ®] , [Google Scholar]] that inverse monoids, though being amalgamation bases in the class of all monoids, may fail to possess this property when put in the ordered scenario. The purpose of the present article is to formulate an ordered version of the Strong Representation Extension Property of Hall and to explore its connections with absolute flatness and amalgamation of pomonoids. This enables us to prove that pogroups are (strong) amalgamation bases in the class of all pomonoids.     

半质环的交换性条件

本文对满足可变恒等式的半质环在某种有界条件下给出了一个判断环Ｒ交换性的简便准则，使文献［２－２７］中所有相应结果均成为其直接推论．此外，对不限有界的情况，也得到较为广泛的结论．