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1.
主要证明了:(i)假设R是右广义半正则右ACS-环,若J(R)∩I=J(I)对于R的任意右理想I都成立,则J(R)=Z(RR);(ii)如果R是右AP-内射环且R的每个奇异单右R-模是GP-内射,则对于R的任意右理想I都有J(R)∩I=J(I). 相似文献
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Li Fuan 《数学年刊B辑(英文版)》1989,10(3):341-350
Let R be an arbitrary commutative ring, and n an integer≥3. It is proved for any ideal J of R thatEO_(2n)(R, J)=[EO_(2n)(R), EO_(2n)(J)]=[EO_(2n)(R), EO_(2n)(R, J)]=[EO_(2n)(R), O_(2n)(R,J)]=[O_(2n)(R), EO_(2n)(R,J)].In particular, EO_(2n)(R, J) is a normal subgroupof O_(2n)(R). Furthermore, the problem of normal subgroups of O_(2n)(R) has an affirmative solution if and only if aR∩ Ann(2)=α~2 Ann(2) for each a in R. In particular, if 2 is not a zero divisor in R, then the problem of normal subgroups of O_(2n)(R) has an affirmative solution 相似文献
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Huanyin CHEN Department of Mathematics Hunan Normal University Changsha China. 《数学年刊B辑(英文版)》2007,28(6):617-628
A ring R is a QB-ring provided that aR bR=R with a,b∈R implies that there exists a y∈R such that a by∈R_q~(-1).It is said that a ring R is a JB-ring provided that R/J(R)is a QB-ring,where J(R)is the Jacobson radical of R.In this paper,various necessary and sufficient conditions,under which a ring is a JB-ring,are established.It is proved that JB-rings can be characterized by pseudo-similarity.Furthermore,the author proves that R is a JB-ring iff so is R/J(R)~2. 相似文献
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A *-ring R is called a nil *-clean ring if every element of R is a sum of a projection and a nilpotent.Nil *-clean rings are the *-version of nil-clean rings introduced by Diesl.This paper is about the nil *-clean property of rings with emphasis on matrix rings.We show that a *-ring R is nil *-clean if and only if J(R) is nil and R/J(R) is nil*-clean.For a 2-primal *-ring R,with the induced involution given by (aij)* =(a*ij)T,the nil *-clean property of Mn(R) is completely reduced to that of Mn(Z2).Consequently,Mn(R) is not a nil *-clean ring for n =3,4,and M2(R) is a nil *-clean ring if and only if J(R) is nil,R/J(R) is a Boolean ring and a*-a ∈ J(R) for all a ∈ R. 相似文献
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设S为有限局部单位元半群,R为S—分次环.首先定义了S—分次环R在半群S上的冲积R#S*,证明了模范畴R#S*-M od与分次模范畴(S,R)-g r之间的等价性,并进一步研究了局部单位元半群分次环的分次Jacobson根及其相关的自反根的关系,得到重要关系式J(R#S*)=JS(R)#S*及Jref(R)=(J(R#S*))↓=JS(R). 相似文献
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J-semicommutative环的性质 总被引:1,自引:0,他引:1
环冗称为J—semicommutative若对任意B,b∈R由ab=0可以推得aRb∈J(R),这里J(R)是环R的Jacobson根.环R是J—semicommutative环当且仅当它的平凡扩张是J—semicommutative环当且仅当它的Don'oh扩张是J—semicommutative环当且仅当它的Nagata扩张是,一semicommutative环当且仅当它的幂级数环是J—semicommutative环.若R/J(R)是semicommutative环,则可得到R是J-semicommutative环.本文进一步论证了如果,是环月的一个幂零理想,且R/I是J—semicommutative环,则R也是J-semicommutative环最后给出了J—semicommutative环与其他一些常见环的联系 相似文献
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一类Jacobi矩阵的逆特征问题 总被引:12,自引:0,他引:12
李珍珠 《高等学校计算数学学报》2002,24(4):298-306
1 引 言n阶实对称矩阵J=若bi>0(i=1,2,…,n-1),称J为Jacobi矩阵,全体记为Jn. Jacobi矩阵的逆特征问题有广泛的应用.文[1]给出了由三个特征对构造相应的Jaco-bi矩阵的逆特征问题有唯一解的条件,但没有考虑到特征对的顺序,也没有给出有解的条件.本文从振动工程的实际出发,提出如下两个问题: 相似文献
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本文的目的,是推广[1]中定理1.22和[2]中命题1(1).我们得到:设R是环,且Q=EndR(M),其中M是广义拟内射模.那么有(1)J(Q)=Z(Q);(2)Q/J(Q)是Von Neumann正则环. 相似文献
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Let
J:\mathbbR ? \mathbbRJ:\mathbb{R} \to \mathbb{R}
be a nonnegative, smooth compactly supported function such that
ò\mathbbR J(r)dr = 1. \int_\mathbb{R} {J(r)dr = 1.}
We consider the nonlocal diffusion problem
$
u_t (x,t) = \int_\mathbb{R} {J\left( {\frac{{x - y}}
{{u(y,t)}}} \right)dy - u(x,t){\text{ in }}\mathbb{R} \times [0,\infty )}
$
u_t (x,t) = \int_\mathbb{R} {J\left( {\frac{{x - y}}
{{u(y,t)}}} \right)dy - u(x,t){\text{ in }}\mathbb{R} \times [0,\infty )}
相似文献
14.
In This paper, the concept of weakly dual ring is introduced, which is a proper generalization of the dual ring. If R is a right weakly dual ring, then (1) Z(RR) = J(R); (2) If R is also a zero-division power ring, then R is a right AP-injective ring. In addition, some properties of weakly dual rings are given. 相似文献
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Firstly,the commutativity of rings is investigated in this paper.Let R be a ring with identity.Then we obtain the following commutativity conditions: (1) if for each x ∈ R\N(R) and each y ∈ R,(xy)k =xkyk for k =m,m + 1,n,n + 1,where m and n are relatively prime positive integers,then R is commutative;(2) if for each x ∈ R\J(R) and each y ∈ R,(xy)k =ykxk for k =m,m+ 1,m+2,where m is a positive integer,then R is commutative.Secondly,generalized 2-CN rings,a kind of ring being commutative to some extent,are investigated.Some relations between generalized 2-CN rings and other kinds of rings,such as reduced rings,regular rings,2-good rings,and weakly Abel rings,are presented. 相似文献
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《代数通讯》2013,41(8):2489-2497
Let (R. m) be a d-dimensional Cohen-Macaulay local ring. Given m-primary ideals J ? I of R such that I is contained in the integral closure of J and λ(I/J)= I, we compare depth G(J) and depth G(J). For example, if J has reduction number one, JI = I2, and μ(J)≤ d + 1, we prove that depth G(I)≥d – 1. If, in addition, μ(I)= d + 1, we show that I has reduction number one, and hence G(I) is Cohen-Macaulay. These results, besides leading to statements comparing depths of associated graded rings along a composition series, make visible the possibility of studying powers of an ideal by using reductions that are not minimal reductions. 相似文献
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L. J. Ratliff Jr. 《Annali di Matematica Pura ed Applicata》1977,112(1):151-192
Summary It is proved that the following statements are equivalent for semi-local domain R:1) R is taut (i.e., for each non-maximal prime ideal P in R, height P+depth P=altitude R).2) Every integral domain which contains and is integral over R is taut.3) R[1/b]. satisfies the second chain condition for prime ideals (s.c.c.), for each non-zero b in the Jacobson radical J of
R.4) R[1/b] satisfies the first chain condition for prime ideals (f.c.c.), for some non-zero b in J.5) For each depth one prime ideal P in R, RP satisfies the s.c.c. and height P=altitude R−1.6) R(X) is taut, where X is an indeterminate.7) For each pair of analytically independent elements b, c in R, R(c/b) is taut and altitude R(c/b)=altitude R−1.8) Each maximal set of analytically independent elements in R contains either one element or altitude R elements. Much of the
theorem is then generalized (with suitable modifications) to rings which contain and are integral over a taut semi-local ring.
Entrata in Redazione il 5 dicembre 1975.
Research on this paper was supported in part by the National Science Foundation grant NSF GP-28939-1. 相似文献
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亚投射环是一类重要的环,它满足比J(R)=0更强的条件,本文的主要目的是回答关于亚投射环的两个问题,进一步获得了关于亚-Grothendieck群的一个结果。 相似文献
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<正> §1.引言 用(z)=(z~1,…,z~n)代表n個複變数,並命z~k=x~k+iy~k,此處x~k,y~k(1≤k≤n)是實數。代表x~1,…,x~n,y~1,…,y~n所定義的2n維空間中的一個域。我們現在並不假定它是受囿,抑單連通等性質。命 相似文献
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