首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到19条相似文献,搜索用时 203 毫秒
1.
证明了一般环I是Clean一般环当且仅当I上的形式幂级数一般环I[[x]]是Clean一般环;一般环I上的多项式环I[x]是Clean一般环当且仅当I是诣零的.引入了强Clean一般环的概念,它是强Clean环的推广.并证明了强π-正则的一般环是强Clean一般环.  相似文献   

2.
推广了唯一强clean环的概念,定义了唯一强clean一般环,得到了唯一强clean一般环的若干性质,并且给出了一般环的三角矩阵环和斜幂级数环是唯一强clean的条件.  相似文献   

3.
崔建  陈建龙 《数学研究》2012,45(2):167-174
称一个环R中的元素a是拟polar元,若存在p2=P∈R满足p∈comm_R~2(a),a+P∈U(R)并且ap∈R~(qnil);且称环R是拟polar的如果R中每一个元素都是拟polar元.本文证明了,任一环R中强π-正则元是拟polar的,而拟polar元是强clean的.拟polar环的一些扩张性质也作了探讨.  相似文献   

4.
环R是强可分的,如果对任意有限生成投射R-模A,B,A⊕A ≌B⊕B,则A≌B.该文证明了置换环上的强可分性在亚直积下是不变量.作为应用,证明了R/(IJ)是强可分的当且仅当R/(I∩J)是强可分的.  相似文献   

5.
引入强3-Armendariz环的概念,研究了它们的性质。给出环R是强3-Armendariz环的充要条件。构造了是强3-Armendariz环但不是幂级数Armendariz环的例子。证明了若环R是约化环,则R[X]/(xn)是强3-Armendariz环,其中(xn)是由xn生成的R[x]的理想。  相似文献   

6.
元α∈R称为近clean的,如果它是幂等元和满元察的和.若环R中的每一个元都是近clean元,则环R称为近clean环.在此定义下,证明了对Abel环R,下列结论是等价的,(1)R是近clean的;(2)(ν)α∈R,Эe=e2∈R,使得V(α)(∈)V(e)且V(1-α)(∈)V(1-e);(3)适中空间Ξ(R)是强零维的;(4)R是pm环且Max(R)是强零维的.某些近clean元的判别也可由此得到.  相似文献   

7.
一般环(未必有单位)中的元素a称为clean,若其可表为一个幂等元和一个Q(R)中元素之和;一般环I称为clean general环,若环I中元素都是clean的.受clean和弱clean指数概念的启发,我们给出对于一般环的一类新的指数——广义弱clean指数,给出该指数的一些性质,并且证明了一般环的广义弱clean指数为1时,该环为abelian环.进一步地,我们给出一般环的广义弱clean指数为2或3时环的性质刻画,得到了一些有关矩阵环的广义弱clean指数的性质.而对于一些在文献中已有的结论,我们给出其推广形式.  相似文献   

8.
关于半交换环与强正则环   总被引:1,自引:0,他引:1  
本文得到了环R是强正则环的若干充分必要条件,证明了下面条件是等价的:(1)R是强正则的;(2)R是半交换正则的;(3)R是半交换的左SF-环;(4)R是半交换的ELT环,且使得每个单左R-模是P-内射的或者平坦的;(5)R是半交换右非奇异的左SF-环;(6)R是半素的半交换左(或右)P-内射环.  相似文献   

9.
设R是一个环,J(R)表示R的Jacbson根.R的一个元素称为强J-clean的,如果能够表示成一个幂等元和一个J(R)中元素的和且这两个元素可交换.对于一个可交换局部环R满足2∈J(R),得到一个在RG上2×2矩阵是强J-clean的充要条件,其中G={1,g}是一个群.同时给出了强clean性的上应用.  相似文献   

10.
胡卫群 《数学杂志》1994,14(4):465-467
强正则环的刻划胡卫群(安徽省滁州师范专科学校)Auslander在[3]中证明了:环A是VonNeumann正则的对于A的任意左理想L与A的任意右理想R,,总有RnL=RL.R.YueChiMing在[2]中推广了Auslander[3]的结果,证明...  相似文献   

11.
We in this note introduce a new concept, so called strongly J-semiclean ring, that is a generalization of strongly J-clean rings. We first observe the basic properties of strongly J-semiclean rings, constructing typical examples. We next investigate conditions on a local ring R that imply that the upper triangular matrix ring T_n(R) is a strongly J-semiclean ring. Also,the criteria on strong J-semicleanness of 2 × 2 matrices in terms of a quadratic equation are given. As a consequence, several known results relating to strongly J-clean rings are extended to a more general setting.  相似文献   

12.
An associative ring with identity R is called Armendariz if, whenever (∑^m i=0^aix^i)(∑^n j=0^bjx^j)=0 in R[x],aibj=0 for all i and j. An associative ring with identity is called reduced if it has no non-zero nilpotent elements. In this paper, we define a general reduced ring (with or without identity) and a general Armendariz ring (with or without identity), and identify a class of maximal general Armendariz subrings of matrix rings over general reduced rings.  相似文献   

13.
Lingling Fan 《代数通讯》2013,41(6):2021-2029
Let R be an associative ring with identity. An element a ∈ R is called clean if a = e + u with e an idempotent and u a unit of R, and a is called strongly clean if, in addition, eu = ue. A ring R is clean if every element of R is clean, and R is strongly clean if every element of R is strongly clean. When is a matrix ring over a strongly clean ring strongly clean? Does a strongly clean ring have stable range one? For these open questions, we prove that 𝕄 n (C(X)) is strongly π-regular (hence, strongly clean) where C(X) is the ring of all real valued continuous functions on X with X a P-space; C(X) is clean iff it has stable range one; and a unital C*-algebra in which every unit element is self-adjoint is clean iff it has stable range one. The criteria for the ring of complex valued continuous functions C(X,?) to be strongly clean is given.  相似文献   

14.
研究了相对于环的自同态的$(b, c)$-逆的相对性质.在更一般地条件下, 定义了一类新的广义逆, 即$\alpha$-$(b, c)$-逆. 通过具体例子说明了$\alpha$-$(b, c)$-逆与$(b, c)$-逆是完全不同的两类广义逆, 并研究了$\alpha$-$(b, c)$-逆与$(b, c)$-逆等价的条件. 此外, 还研究了$\alpha$-$(b, c)$-逆的强clean分解. 这些研究结果统一和推广了$(b, c)$- 逆上的若干已知结果.  相似文献   

15.
Let R be a commutative local ring. It is proved that R is Henselian if and only if each R-algebra which is a direct limit of module finite R-algebras is strongly clean. So, the matrix ring 𝕄 n (R) is strongly clean for each integer n > 0 if R is Henselian and we show that the converse holds if either the residue class field of R is algebraically closed or R is an integrally closed domain or R is a valuation ring. It is also shown that each R-algebra which is locally a direct limit of module-finite algebras, is strongly clean if R is a π-regular commutative ring.  相似文献   

16.
It is well known that every uniquely clean ring is strongly clean. In this article, we investigate the question of when this result holds element-wise. We first construct an example showing that uniquely clean elements need not be strongly clean. However, in case every corner ring is clean the uniquely clean elements are strongly clean. Further, we classify the set of uniquely clean elements for various classes of rings, including semiperfect rings, unit-regular rings, and endomorphism rings of continuous modules.  相似文献   

17.
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.  相似文献   

18.
环$R$称为是半clean的, 是指环中的每个元素都是一个单位与一个周期元的和. clean环是半clean的. 刻画半clean群环的一般情形是不容易的. 我们的目的是考虑如下问题:若$G$ 是局部有限群或者是阶是3的循环群, 群环$RG$何时是semiclean的. clean群环上的一些已有结果被推广.  相似文献   

19.
Lingling Fan 《代数通讯》2013,41(3):799-806
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 : 35833592 .[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.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号