分次环的有限正规张

本文研究了群分次环的有限正规分次扩张问题.利用经典环论方法,得到一个群分次环与其有限正规分次扩张环之间关于分次Jacobson根和分次素根的关系,同时,给出了分次情形的Cutting down定理和Lying over定理.     

分次Morita Contexts与分次根

设M={A=⊕_(g∈G)A_g,V=⊕_(g∈G)V_g,W=⊕_(g∈G)W_g,B=⊕_(g∈G)B_g}与(,),[,]是一个G-分次Morita Context,且满足(V,W)=A,[W,V]=B,A,B都有单位元．本文证明τG(B)：[W,ΥG(A)V]=【WΥc(A),V],ΥG(A)=(V,ΥG(B)W)=(VΥG(B),W)其中ΥG代表P_G(分次素根),J_G(分次Jacobson根),K_G(分次Koethe根),L_G(分次Levitzki根)和s_G(分次强素根),us_G(分次一致强素根)．     

分次环的分次Excellent扩张

本文引进了分次环的分次Excellent扩张概念,设S=⊕_(g∈G)S_g是R=⊕_(g∈G)R_g的分次Excellent扩张,证明了S是分次右V-环当且仅当R是分次右V-环,S是分次PS-环当且仅当R是分次PS-环,S是分次Von Neumann正则环当且仅当R是分次Von Neumann正则环。     

群分次环的分次Levitzki根

建立了分次环的分次Levitzki根,并给出了分次Levitzki半单环的结构定理及相关结果.     

环的根性质

研究的对象是不含单位元分次环 R,首先证明了有关 Jacobson根的重要性质 J( R) =J( S)∩ R,其中 S =R× Z.然后利用它得到了一些好的性质     

有限群分次环上的余挠对研究

本文研究了余挠对在有限群分次和非分次情况下的联系.利用分次理论以及相对同调,我们首先研究了R是任意环G是有限群的情况下,余挠对在R-模范畴以及斜群环S=R*G-模范畴之间的关系;然后我们研究了R-gr范畴中刚性余挠对的等价刻画,同时给出了余挠对在R-gr范畴与R-模范畴之间的关系,其中R是G分次环,群G是有限群且|G|^-1∈R.     

分次环的分次σ-根

在分次环类中定义H-关系,利用H-关系给出分次σ-根的定义,并进一步得到分次环类γ是分次σ-根的几个充分必要条件.     

群分次环与群分次模的基座

将关于交叉积的基座的主要结果推广到了群分次环上，得到了群分次环的基座的一些具体刻划，特别地，证明了对有限群G和强G－分次环R，有Soc(RR) Soc(ReRe)R soc^ ｜G｜（RR）。     

关于挠自由群分次环的注记

本文推广ＣＮａｓｔａｓｅｃｕ，Ｆ．ＶａｎＯｙｓｔａｅｙｅｎ的有关结果，并在一定条件下回答了Ｋ．Ｒ．Ｆｕｌｌｅｒ等人的公开问题．     

LENGTH ONE IDEAL EXTENSIONS AND THEIR ASSOCIATED GRADED RINGS

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.     

分次环的分次根(英文)

本文建立了分次环的分次Baer根及分次Koethe根.利用根的结构定理,给出了相应半单分次环的结构定理.     

GRADED RINGS OF LOCAL FINITE REPRESENTATION TYPE

Abstract

Graded Artin algebras whose category of graded modules is locally of finite representation type are introduced. The representation theory of such algebras is studied. In the hereditary case and in the stably equivalent to hereditary case, such algebras are classified.     

Semiregular Morphisms

If M and N are modules, the concept of semiregularity (and regularity) of hom(M,N) is defined and studied, and the connection with the relative direct injective- and direct projective-properties is established. The relationship of semiregularity to the Jacobson radical of hom(M,N), to the singular and cosingular ideals of hom(M,N), and to the notion of lying over or under a direct summand, is described, and the basic results in the module case are extended.

Communicated by R. Wisbauer.     

On (Semi)Regular Morphisms

Let M and N be right R-modules. Hom(M, N) is called regular if for each f ∈ Hom(M, N), there exists g ∈ Hom(N, M) such that f = fgf. Let [M, N] = Hom _R (M, N). We prove that if M is finitely generated, then [M, N] is regular if and only if every homomorphism M → N is locally split. In this article, we also study the substructures of Hom(M, N) such as the Jacobson radical J[M, N], the singular ideal Δ[M, N], and the co-singular ideal ?[M, N]. We prove several new results. The question is to characterize when the Jacobson radical is equal to the singular ideal Δ[M, N] or the co-singular ideal ?[M, N] under injectivity and projectivity.     

流线扩散有限元方法在分层网格上的收敛性分析

本文在分层网格上分析了采用线性元的流线扩散有限元方法求解一维对流扩散型奇异摄动问题的一致收敛性.在ε≤N~(-1)的前提下,可以证明在SD范数下的一致误差估计为O(N~(-1)(log 1/ε)~2)在数值算例部分对理论结果进行了验证.     

有限置换模自同态环的可分性质

设Q是有限置换右R模,则End_R(Q)是可分环当且仅当对所有A,B∈FP(Q),A AA B B B A≤ B或 B≤A,作为应用得到了 End_R(P Q)是可分环当且仅当End_R P和End_R Q为可分环,其中P,Q为有限置换右R模。