关于拟Koszul模的注记

对于每个诺特半完全代数A上的模M,都有一个谱序列E_（pq）～＊（M）与之相对应.本文证明了有限生成A-模M是拟Koszul的当且仅当谱序列E_（pq）～＊（M）的第E～2层是平凡的.与之对偶,本文叙述了余拟Koszul模情况下的类似结果.     

具有d-Koszul子模滤的分次模

引入了弱d-Koszul模,它是d-Koszul模的一种自然推广.设A是d-Koszul代数,M是有限生成的分次A-模,则M是弱d-Koszul模当且仅当M具有子模滤 0(∪) U0(∪)U1(∪)…(∪)Up=M,使得所有的A-模 Ui/Ui-1是d-Koszul模.设M为一个弱d-Koszul模,则作为分次Ext*A(A0,A0)-模,其Koszul对偶,ε(M)=Ext*A(M,A0)是由0次生成的.     

球面稳定同伦群的两个新元素h0(b1)3(γ)s和(b1)3g0(γ)s

本文证明了当p(＞-)11,3(<-)s＜p-3时,h0(b1)3∈Ext7,3p2q+qA(H*V(2),Zp),(b1)3g0∈Ext8,3p2q+pq+2q(H*V(2),Zp)在Adams谱序列中分别收敛到π*V(2)的非零元,h0(b1)3(γ)s∈Ext7+s,(s+3)p2q+(s-1)pq+(s-3)A(Zp,Zp)在Adams谱序列中分别收敛到π*S的非零p阶元.     

乘积元b0g0(γ)s在Adams谱序列中的收敛性

决定球面稳定同伦群是同伦中的一个中心问题,同时也是非常困难的问题之一.Adams谱序觌是其计算的最有效的工具.在本文,令p>5为素数,A表示模p的Steenrod代数.我们利用Adams谱序列和May谱序列证明了,在球面稳定同伦群π*S中,存在一族在Adams谱序列中由b0g0γs∈Exts+4,sp2q+(s+1)pq+sq+s-3A(ZpZp)所表示的新的非平凡元素,其中q=2(p-1),3≤s相似文献   

球面稳定同伦群中的一族新元素及h0b12在π*V(1)中的收敛性

对连通有限型谱X,Y,存在着Adams谱序列(ASS){Ers,t,dr}满足(1)drErs,t→Ers+r,t+r-1是谱序列的微分,(2)E2s,t≌ExtAs,t(H*(X),H*(Y)),(3)并且收敛到[∑t-sY,X]p.当X是球谱S,Moore谱M,Toda-Smith谱V(1)时,(πt-sX)p分别为S,M,V(1)的稳定同伦群.本文通过Adams谱序列,发现了球谱S的稳定同伦群中的一族非零元素~γth0b02及Toda-Smith谱V(1)的稳定同伦群中的非零元素h0b12.在利用Adams谱序列求解同伦群的过程中,需要计算有关ExtAs,t(H*X,H*Y)的结果.利用谱的上纤维序列导出的Ext群的正合序列和May谱序列,得出ExtAs,t(H*X,H*Y)的某些结果.本文令p≥7为奇素数,q=2(p-1).     

球面稳定同伦群的两个新元素h_0(b_1)~3_s)和(b_1)~3g_0_s)

本文证明了当p≥11,3≤s相似文献   

球面稳定同伦群的两个新元素h0(b1)3(γ)s和(b1)3g0(γ)s

本文证明了当p(＞-)11,3(<-)s＜p-3时,h0(b1)3∈Ext7,3p2q+qA(H*V(2),Zp),(b1)3g0∈Ext8,3p2q+pq+2q(H*V(2),Zp)在Adams谱序列中分别收敛到π*V(2)的非零元,h0(b1)3(γ)s∈Ext7+s,(s+3)p2q+(s-1)pq+(s-3)A(Zp,Zp)在Adams谱序列中分别收敛到π*S的非零p阶元.     

有限复杂度的Koszul代数

首先给出了Koszul代数的张量积的复杂度,然后研究了Koszul遗传代数上的Koszul单列模,并证明了Koszul遗传代数上的Koszul模M的Koszul合成列在同构意义下是唯一的.     

弱分段Koszul模(英文)

任意一个弱分段Koszul模M都被证明存在一个自然的分次子模链0=U₀（?）U₁（?）U₂（?）…（?） U_t=M使得每个商U_i/U_i-1都是分段Koszul模.本文的主要目的是建立M和U_i/U_i-1的极小分次投射解之间的关系.对n≥0,证明了P_n=⊕_i=1^t P_nⁱ,其中P_*ⁱ→U_i/U_i-1→0和P_*→M→0是相应的极小分次投射解,作为其直接推论,有pd（M）=max{pd(U_i/U_i-1)}成立.     

大族长度为pq的伪随机k元序列

Mauduit与Sárkzy在一系列论文中研究了κ元序列的伪随机性.本文通过对模pq剩余类环Z_(pq)进行分割,进而结合离散对数的方法,构造了一大族长度为pq的伪随机κ元序列,并证明其具有很好的伪随机性.     

Strongly rational comodules and semiperfect Hopf algebras over QF rings

Let C be a coalgebra over a QF ring R. A left C-comodule is called strongly rational if its injective hull embeds in the dual of a right C-comodule. Using this notion a number of characterizations of right semiperfect coalgebras over QF rings are given, e.g., C is right semiperfect if and only if C is strongly rational as left C-comodule. Applying these results we show that a Hopf algebra H over a QF ring R is right semiperfect if and only if it is left semiperfect or — equivalently — the (left) integrals form a free R-module of rank 1.     

Stable Projective Homotopy Theory of Modules,Tails, and Koszul Duality

A contravariant functor is constructed from the stable projective homotopy theory of finitely generated graded modules over a finite-dimensional algebra to the derived category of its Yoneda algebra modulo finite complexes of modules of finite length. If the algebra is Koszul with a noetherian Yoneda algebra, then the constructed functor is a duality between triangulated categories. If the algebra is self-injective, then stable homotopy theory specializes trivially to stable module theory. In particular, for an exterior algebra the constructed duality specializes to (a contravariant analog of) the Bernstein–Gelfand–Gelfand correspondence.     

广义幂级数环的Morita对偶

设A,B是有单位元的环, (S,≤)是有限生成的Artin的严格全序幺半群, AMB是双模.本文证明了双模[[AS,≤]][MS,≤][[BS,≤]]定义一个Morita对偶当且仅当 AMB定义一个Morita对偶且A是左noether的,B是右noether的.因此A上的广 义幂级数环[[AS,≤]]具有Morita对偶当且仅当A是左noether的且具有由双模AMB 诱导的Morita对偶,使得B是右noether的.     

Complete flat modules

Let R be a commutative and noetherian ring. It is known tht if R is local with maximal ideal M and F is a flat R-module, then the Hausdorff completion F of F with the M-adic topology is flat. We show that if we assume that the Krull dimension of R is finite, then for any ideal I C R, the Hausdorff completion F* of a flat module F with the I-adic topology is flat. Furthermore, for a flat module F over such R, there is a largest ideal I such that F is Hausdorff and complete with the I-adic topology. For this I, the flat R/I-module F/IF will not be Hausdorff and complete with respect to the topology defined by any non-zero ideal of R/I. As a tool in proving the above, we will show that when R has finite Krull dimension, the I-adic Hausdorff completion of a minimal pure injective resolution of a flat module F is a minimal pure injective resolution of its completion F*. Then it will be shown that flat modules behave like finitely generated modules in the sense that on F* the I-adic and the completion topologies coincide, so F* is I-adically complete.     

Noetherian Semigroup Algebras

A complete structural characterization of submonoids S of apolycyclic-by-finite group such that the semigroup algebra K[S]over a field K is right noetherian is obtained. It follows thatsuch algebras are also left noetherian. 2000 Mathematics SubjectClassification 16P40, 16S36, 20M25 (primary), 20F22, 20C07,20M10 (secondary).     

量子代数模的张量积与不可分解模

令M是Z[v]的由v-1和奇素数p生成的理想,U是A=Z[v]M上相伴于对称Cartan矩阵的量子代数.k是特征为零的代数闭域,A→k(v(?)ξ)是环同态.U_k=U(?)_Ak,u_k是U_k的无穷小量子代数.令ξ是1的p次本原根.本文证明了:若有限维可积U_k模M,V中至少有一个是内射模,或者M,V中有一个模作为u_k模是平凡的,则有U_k模同构M(?)V≌V(?)M.我们还证明了:若有限维可积U_k模V作为u_k模是不可分解的,有限维可积U_k模M是不可分解的,且M|_(uk)是平凡的,则V(?)M是不可分解U_k模.令V和M是有限维可积U_k模,作为u_k模是同构的且具有单基座,本文证明V和M作为U_k模也是同构的.由此得到:不可分解内射u_k模提升为U_k模是唯一的.     

一类Witt代数的包络代数的表示

设C为复数域,P,q∈C,且pq是m次本原单位根．我们构造了一个Zm-分次模类V(a,b),它为Witt代数的包络代数的(P,q)变形U(Wpq)的Zm-分次模类,并证明了任何一个Zm-分次U(Wpq)-模都与某个V(a,b)同构．     

H~＊－有理模和右Smash积A＃~R_HH~＊ 

本文对Ｈ￣＊上的有理模Ｍ做了一些讨论，刻划了此类模的某些性质，并利用这些性质得到了右Ｓｍａｓｈ积Ａ＃［ｋＧ］上模Ｍ是完全可约模的条件。     

Quasi-Frobenius Rings and Nakayama Permutations of Semiperfect Rings

We say that is a ring with duality for simple modules, or simply a DSM-ring, if, for every simple right (left) -module U, the dual module U* is a simple left (right) -module. We prove that a semiperfect ring is a DSM-ring if and only if it admits a Nakayama permutation. We introduce the notion of a monomial ideal of a semiperfect ring and study the structure of hereditary semiperfect rings with monomial ideals. We consider perfect rings with monomial socles.