共查询到20条相似文献,搜索用时 31 毫秒
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Fang Gui WANG Institute of Mathematics Software Science Sichuan Normal University Sichuan P.R.China 《数学研究与评论》2010,(3)
Let R be a domain and let R wg be the w-global transform of R.In this note it is shown that if R is a Mori domain,then the t-dimension formula t- dim(R wg ) = t- dim(R) - 1 holds. 相似文献
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Let R be an associative ring with identity.R is said to be semilocal if R/J(R)is(semisimple)Artinian,where J(R)denotes the Jacobson radical of R.In this paper,we give necessary and sufficient conditions for the group ring RG to be semilocal,where G is a locally finite nilpotent group. 相似文献
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设R是有1的交换环,2是R的单位.本文决定了R上李代数sl2(R)的理想.进而,若R是整环,本文决定了sl2(R)与gl2(R)的自同构形式. 相似文献
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1984年,Ho Kuen Ng在[1]中给出了交换环与模的有限表现维数(简称为F.P.—维数)的定义及若干有意义的重要结果.从此,有限表现性的讨论成为环论的热门课题之一.作者在[2]中将有限表现维数推广到非交换环上.并利用有限表现维数刻划了凝聚环,在[3]中讨论了有限表现维数的换环定理.在[4]中讨论了笛卡尔方形上的有限表现维数.丁南庆在[5]中推广了有限表现维数,给出了一种新维数——模的有限生成维数,在[6]中讨论了有限表现模的对偶 相似文献
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Fang Gui WANG 《数学研究与评论》2010,30(3)
Let R be a domain and let Rωg be the ω-global transform of R. In this note it is shown that if R is a Mori domain, then the t-dimension formula t- dim(Rωg) = t-dim(R)-1 holds. 相似文献
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本文讨论了微商共同作用在半素环的某个Lie理想上的问题。给出了如下结果:设R是带有中心Z(R)的半素环,Qmr是R的极大右商环,L是R的非交换Lie理想,d和δ是R的微商,假设rR(「L,L」)=0且d(x)x-xδ(x)∈Z(R)对任意x∈L成立,则在R的扩张形心C中存在一个幂等元e使得d(1-e)Qmr=0和δ(1-e)Qmr)=0并且eQmr满足S4。另外给出微商共同作用在半素环上多项式的结 相似文献
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设R是一个含有单位元的2无扰的交换环,M_2(R)是定义在R上的全矩阵代数,证明了M_2(R)上的每一个非线性Lie导子都可以表示成一个内导子,一个可加诱导导子和一个映所有二次换位子为零的中心映射的和. 相似文献
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Let α be a nonzero endomorphism of a ring R, n be a positive integer and T_n(R, α) be the skew triangular matrix ring. We show that some properties related to nilpotent elements of R are inherited by T_n(R, α). Meanwhile, we determine the strongly prime radical, generalized prime radical and Behrens radical of the ring R[x; α]/(x~n), where R[x; α] is the skew polynomial ring. 相似文献
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交换主理想整环上立方幂等矩阵的线性保持 总被引:1,自引:0,他引:1
设R(≠F_3)是特征不为2的交换主理想整环,M_n(R)定义R上的n×n矩阵模,本文刻划当n≥m时从M_n(R)到M_n(R)的保持立方幂等矩阵的线性映射的形式,由此推广了Chan和Lim的一个结果([1,定理3]). 相似文献
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《Quaestiones Mathematicae》2013,36(1):73-89
Abstract Transcendental and algebraic elements over commutative rings are defined. Rings with zero nil radical are considered. For a transcendental over R, necessary and sufficient conditions are derived for elements of R[α] to be algebraic or transcendental over R. For R a ring with identity and a finite number of minimal prime ideals, necessary and sufficient conditions are given for any element in a unitary overring of R to be algebraic or transcendental over R. It is proved that if α is algebraic Over R, so is every element of R[α]. It is show that if R is Noetherian, β is algebraic over R[α] and α is algebraic over R, then, under certain conditions, β is algebraic over R. If R has a finite number of minimal prime ideals, P1,…,Pk, which are pairwise comaximal, then if t is transcendental over R, R[t] can be obtained by adjoining k algebraic elements ai over R to R whose defining polynomials are in Pi [x], and conversely, if such elements are adjoined to R, they generate an element transcendental over R. 相似文献
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交换环上的严格上三角矩阵代数上的Lie导子 总被引:1,自引:0,他引:1
设R是任意含单位元的交换环,N(R)为R上(n+1)×(n+1)严格上三角矩阵构成的代数.本文证明了当n≥3且2是R的单位时,N(R)上任意Lie导子D可以唯一的表示为D=D_d+D_b+D_c+D_x,其中D_d,D_b,D_c,D_x分别是N(R)上的对角,极端,中心和内Lie导子,在n=2的情况,我们也证明了N(R)上任意Lie导子D可以表示为对角,极端,内Lie导子的和。 相似文献
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Let R be a commutative ring and Г(R) be its zero-divisor graph.We com-pletely determine the structure of all finite commutative rings whose zero-divisor graphs have clique number one,two,or three.Furthermore,if R≌ Ri × R2 × … Rn (each Ri is local for i =1,2,3,…,n),we also give algebraic characterizations of the ring R when the clique number of r(R) is four. 相似文献
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具有奇异值分解性质的代数 总被引:4,自引:0,他引:4
设F为一个域,R为一个带有对合的F-代数,如果R上每一个矩阵都有奇异值分解(简称SVD),则称R为一个有SVD性质的F-代数.本文指出:R为一个有SVD性质的F-代数的充要条件是:R同构于R~+,或R~+上二次扩域,或R~+上四元数体((-1,-1)/R~+),其中R~+为R的对称元集合,并且R~+为一个Galois序闭域. 相似文献
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Margaret H. Kleinfeld 《代数通讯》2013,41(13):1369-1373
In non-associative rings the associative law is replaced by various weaker identities. In this paper the identity x.yz = z.yx is considered. Let R be a ring satisfying this identity. It is obvious that if R has an identity element, then R is both commutative and associative. It is shown that if R is prime, third power associative, 2-torsion free, and has a nonzero idempotent, then this idempotent must be an identity and hence R must be commutative and associative. 相似文献
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由n次幂等矩阵确定的交换幺半群 总被引:1,自引:0,他引:1
设R是含幺结合环,n≥2为自然数.对所有的k≥1,本文给出了n次幂等矩阵集Pk^n(R)={P|P^n=P∈Mk(R)}上的一种等价关系,证明了P^n(R)=∪k=1^∞Pk^n(R)中的等价类在给定的加法运算下构成一个交换幺半群. 相似文献
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证明了自反Banach空间X上的等价w2R范数全体构成一个剩余集;同时证明了X闭子空间上等价的w2R范数均可延拓为X上等价的w2R范数.特别地,当X是可分时,上述w2R范数可替换为2R范数. 相似文献
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设R是一个含单位元的可交换2-无挠环,且M_n(R)是R上的n×n阶矩阵代数.本文证明了M_n(R)(n≥2)上的满足Φ(ABA)=Φ(A)BA+AΦ(B)A+ABΦ(A)的映射Φ具有形式:存在T∈M_n(R)和R上的一个可加导子φ,使得对任意A= (a_(ij))∈M_n(R),有Φ(A)=AT-TA+A_φ,这里A_φ=(φ(a_(ij))). 相似文献