N-弱拟Armendariz环

本文研究了N-弱拟Armendariz环的基本性质以及与一些特殊环的关系.利用某些矩阵环的特殊性质,得到了环R是N-弱拟Armendariz环当且仅当环T_n(R)是N-弱拟Armendariz环,推广了弱拟-Armendariz环的相应结果.     

广义弱Armendariz环及其扩张（英文）

对环R的一个自同态α,通过引入α-弱Armendariz环和α-弱拟Armendariz环研究了R相对于α的弱Armendariz性质.这两类环是对弱Armendariz环和弱拟Armendariz环的进一步推广,为研究环的弱Armendariz性质提供了新思路.本文对这两类环给出了一些刻画,构造了一些所需的例子和反例,统一和推广了一些已知的研究结果.     

斜诣零Armendariz环

本文研究了α-诣零Armendariz环的性质.利用环R上的斜多项式环,得到了α-诣零Armendariz环的例子并研究了它的扩张,推广了文献[4]中关于诣零Armendariz环的相应的结论.     

环的Armendariz性

研究了一个环何时具有Armendariz性．使用环论的一般方法,证明了在一定条件下商环、具有一对零同态的Morita Context环以及映射环是Armendariz环,推广了已有的某些结果．     

斜诣零Armendariz环

本文研究了α-诣零Armendariz 环的性质. 利用环R 上的斜多项式环, 得到了α-诣零Armendariz 环的例子并研究了它的扩张, 推广了文献[4] 中关于诣零Armendariz 环的相应的结论.     

关于正规GPP环

本文探讨正规ＧＰＰ环的内刻划，并证明正规ＧＰＰ环Ｒ左右对称的一个充分条件是Ｒ为ＧＰ－内射     

交换局部环上的强拟诣零clean2×2矩阵

本文研究了交换局部环上的2阶矩阵的强拟诣零clean性,利用矩阵的特征方程的方法,给出了交换局部环上的2阶矩阵是强拟诣零clean的具体判别方法,所得结果丰富并推广了强拟诣零clean的研究.     

分次Armendariz环与P.P.环

引进分次Armendariz环的概念,讨论了分次环R= n∈2Rn及由它导出的非分次环R,R0,及R[x]之间关于Armendariz环性质的关系,并推广了[8]的结论,得到在R= n∈ZRn是Z-型正分次环的前提下,若R是分次Armendariz,分次正规环,则R是P．P环（Bear环）当且仅当R是分次P．P．环（分环Baer环）。     

斜Armendariz矩阵环

Let R be a ring.We show in the paper that the subring Un(R) of the upper triangular matrix ring Tn(R) is α-skew Armendariz if and only if R is α-rigid,also it is maximal in some non α-skew Armendariz rings,where α is a ring endomorphism of R with α(1) = 1.     

On Skew Inverse Laurent-Serieswise Armendariz Rings

We study the skew inverse Laurent-serieswise Armendariz (or simply, SIL-Armendariz) condition on R, a generalization of the standard Armendariz condition from polynomials to skew inverse Laurent series. We study relations between the set of annihilators in R and the set of annihilators in R((x ^?1; α)). Among applications, we show that a number of interesting properties of a SIL-Armendariz ring R such as the Baer and the α-quasi Baer property transfer to its skew inverse Laurent series extensions R((x ^?1; α)) and vice versa. For an α-weakly rigid ring R, R((x ^?1; α)) is a left p.q.-Baer ring if and only if R is left p.q.-Baer and every countable subset of S _?(R) has a generalized countable join in R. Various types of examples of SIL-Armendariz rings is provided.     

A Note on Compositions of Derivations of Prime Rings

Abstract

In this note we discuss when compositions of derivations can be nonzero derivations of prime rings. In particular we answer two questions posed by Lanski.     

强哈密尔顿连通有向图的一个注记

利用收缩技术,证明了1)阶为n=2k且最小半度至少是k的有向图D是强哈密尔顿连通的,除非D属于某些图类;2)2强连通且包含n个顶点、(n-1)(n-2)+4条弧的有向图是强哈密尔顿连通的,除非D属于某些图类.     

强正则自补图的一个注记

Kotzig put forward a question on strongly-regular self-complementary graphs, that is, for any natural number k, whether there exists a strongly-regular self- complementary graph whose order is 4k 1, where 4k 1=x2 y2, x and y are positive integers; what is the minimum number that made there exist at least two non-isomorphic strongly-regular self-complementary graphs. In this paper, we use two famous lemmas to generalize the existential conditions for strongly-regular self-complementary circular graphs with 4k 1 orders.     

A Note on Strongly Clean Matrix Rings

Let R be an associative ring with identity. An element a ∈ R is called strongly clean if a = e + u with e ² = e ∈ R, u a unit of R, and eu = ue. A ring R is called strongly clean if every element of R is strongly clean. Strongly clean rings were introduced by Nicholson [7 Nicholson , W. K. ( 1999 ). Strongly clean rings and Fitting's lemma . Comm. Algebra 27 : 3583 – 3592 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]]. It is unknown yet when a matrix ring over a strongly clean ring is strongly clean. Several articles discussed this topic when R is local or strongly π-regular. In this note, necessary conditions for the matrix ring 𝕄 _n (R) (n > 1) over an arbitrary ring R to be strongly clean are given, and the strongly clean property of 𝕄₂(RC ₂) over the group ring RC ₂ with R local is obtained.     

强symmetric环

为了统一交换环和约化环的层表示,Lambek引进了Symmetric环.继续symmetric环的研究,定义引入了强symmetric环的概念,研究它的一些扩张性质.证明环R是强symmetric环当且仅当R[x]是强symmetric环当且仅当R[x;x~(-1)]是强symmetric环.也证明对于右Ore环R的经典右商环Q,R是强symmetric环当且仅当Q是强symmetric环.     

On Almost Armendariz Ring

In this paper,we introduce the notion of an almost Armendariz ring,which is a generalization of an Armendariz ring,and discuss some of its properties.It has bee...     

Ore Extensions of Skew Armendariz Rings

Let α be an endomorphism and δ an α-derivation of a ring R. We introduce the notion of skew-Armendariz rings which are a generalization of α-skew Armendariz rings and α-rigid rings and extend the classes of non reduced skew-Armendariz rings. Some properties of this generalization are established, and connections of properties of a skew-Armendariz ring R with those of the Ore extension R[x; α, δ] are investigated. As a consequence we extend and unify several known results related to Armendariz rings.