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设R和T是Noether完备半局部环,R→T是环同态.本文证明了,若T是有限生成或ArtinR-模,M为G-Matlis自反R-模,则对所有n≥0,ExtRn(T,M),ExtRn(M,T),TorRn(T,M)以及TorRn(M,T)均是G-Matlis自反T-模.所得结果推广了R.Belshof的结果. 相似文献
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定理1设R是半值环,n为固定的正整数,如果R满足条件:存在依赖于(?)x,y的两个字k(X,Y),t(X,Y),其中|k|X>1,|t|X=1,|k|Y≥|t|Y,|t|Y≤n,使k(x,y)-t(x,y)∈I(R),则R是交换环。定理2设R是半值环,如果R满足条件:存在正整数m=m(x,y)>1,n=n(y),使得(xny)m-x 相似文献
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投影下的Gronwall不等式 总被引:7,自引:1,他引:6
本文对J.K.Hale曾提出的一类广泛的投影下的Gronwal不等式问题作了讨论,对满足u(t)≤a(t)+∫0tb(t-s)u(s)ds+∫0∞c(s)u(t+s)ds,(?)t≥0的函数u(t)∈Cb0(R+,R+)作了估计.其结果对讨论微分方程的有界解、不变流形及其Foliation和进一步讨论奇性Gronwal不等式都有意义 相似文献
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研究(?)Ri的由Ri(i=1,2,…,p)的序所诱导的序,证明(?)Ri在一定条件下作成一个有单位元的f环,并在有单位元的K-f环上的格序模范畴中引入保格R1(?)R2映射,进一步定义了张量积,使张量积概念在不同序环的序模范畴得到拓展. 相似文献
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本文讨论了关于树对完全图删去一些相交的三阶路的广义Ramsey数R(Tm,Kn-tP3)和关路对完全图删去一些不相交的三阶完全图的广义Ramsey数R(Pm,Kn-tK3),获得如下结果:1.如果m≥3,n≥3,那么R(Tm,Kn-tP3)=(m-1)(n-t-1)+1,0≤t≤[n/3].2.若m≥4,n,T≥1,则R(Pm,Kn-tK3)=(m-1)(n+2t-1)+1.从而,这两个结果部分地回答了1983年R.J.Gould和M.S.Jacobson在[1]中提出的未解决问题. 相似文献
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主左理想由若干个幂等元生成的环 总被引:1,自引:0,他引:1
环R称为左PI-环,是指R的每个主左理想由有限个幂等元生成.本文的主要目的是研究左PI-环的von Neumann正则性,证明了如下主要结果:(1)环R是Artin半单的当且仅当R是正交有限的左PI-环;(2)环R是强正则的当且仅当R是左PI-环,且对于R的每个素理想P,R/P是除环;(3)环R是正则的且R的每个左本原商环是Artin的当且仅当R是左PI-环且R的每个左本原商环是Artin的;(4)环R是左自内射正则环且Soc(RR)≠0当且仅当R是左PI-环且它包含内射极大左理想;(5)环R是MELT正则环当且仅当R是MELT左PI-环. 相似文献
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文中研究了Γ-环M与其矩阵环Γn,m-环Mm,n根的关系,得到了:QN(Mm,n)(?)(QN(M))m,n;K(Mm,n)(?)(K(M))m,n.这里QN-根是Γ-环元素的强幂零性所确定的根,K-根是诣零根 相似文献
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Miao-Sen Chen 《Southeast Asian Bulletin of Mathematics》2000,24(1):25-29
In this paper, we shall discuss the conditions for a right SC right CS ring to be a QF ring. In particular, we prove that if R is a right SI right CS ring satisfying the reflexive orthogonal condition (*) and if every CS right R-module is -CS, then R is a QF ring.AMS Subject Classification (1991): 16L30 16L60 相似文献
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François Couchot 《代数通讯》2013,41(2):346-351
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
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Lambek extended the usual commutative ideal theory to ideals in noncommutative rings, calling an ideal A of a ring R symmetric if rst ∈ A implies rts ∈ A for r, s, t ∈ R. R is usually called symmetric if 0 is a symmetric ideal. This naturally gives rise to extending the study of symmetric ring property to the lattice of ideals. In the process, we introduce the concept of an ideal-symmetric ring. We first characterize the class of ideal-symmetric rings and show that this ideal-symmetric property is Morita invariant. We provide a method of constructing an ideal-symmetric ring (but not semiprime) from any given semiprime ring, noting that semiprime rings are ideal-symmetric. We investigate the structure of minimal ideal-symmetric rings completely, finding two kinds of basic forms of finite ideal-symmetric rings. It is also shown that the ideal-symmetric property can go up to right quotient rings in relation with regular elements. The polynomial ring R[x] over an ideal-symmetric ring R need not be ideal-symmetric, but it is shown that the factor ring R[x]/xnR[x] is ideal-symmetric over a semiprime ring R. 相似文献
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Nielsen [29] proved that all reversible rings are McCoy and gave an example of a semicommutative ring that is not right McCoy. When R is a reversible ring with an (α, δ)-condition, namely (α, δ)-compatibility, we observe that R satisfies a McCoy-type property, in the context of Ore extension R[x; α, δ], and provide rich classes of reversible (semicommutative) (α, δ)-compatible rings. It is also shown that semicommutative α-compatible rings are linearly α-skew McCoy and that linearly α-skew McCoy rings are Dedekind finite. Moreover, several extensions of skew McCoy rings and the zip property of these rings are studied. 相似文献
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如果R中每个元素(对应地,可逆元)均可表示为一个幂等元与环R的Jacobson根中一个元素之和,则称环R是J-clean环(对应地,UJ环).所有的J-clean环都是UJ环.作为UJ环的真推广,本文引入GUJ环的概念,研究GUJ环的基本性质和应用.进一步地,研究每个元素均可表示为一个幂等元与一个方幂属于环的Jacobson根的元素之和的环. 相似文献
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具有一对零态射的Morita Context 环(Ⅱ) 总被引:1,自引:0,他引:1
设(A,B,V,W,ψ,φ)是一个Morita Context,具有一对零态射ψ=0,φ=0,C= (A V W B)是对应的Morita Context环.本文给出了C与A,B,V,W之间关于环的π-正则性、semiclean性、Mophic性和环的Exchgange性、Potent性、GM性的关系. 相似文献
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Morphic环和G-morphic环的一些结果 总被引:3,自引:1,他引:2
讨论了morphic环,G-morphic环,PP环,GPP环,Bear环与正则环之间的关系.还证明了在约化环中,强正则环,正则环,π-正则环,G-π-正则环的等价性. 相似文献