极小条件环中的左理想的因子分解

极小条件环中的左理想的因子分解王元金（辽宁师范大学数学系，大连１１６０２２）关键词交换环，素理想，左理想．分类号ＡＭＳ（１９９１）１３Ａ１５／ＣＣＬＯ１５３．３文献［１］讨论了极小条件环中左理想分解为左素理想之交的问题．本文利用文献［１］的一些结果，...     

实有限可除代数间保矩阵M—P逆的共变算子对

设Ｄ,Ｄ１ 和Ｄ２ 是实有限可除代数,Ｍｍｎ（Ｄ）是Ｄ上所有ｍ ×ｎ矩阵的Ｒ线性空间． 若两个Ｒ线性算子ｆ：Ｍｍ ｎ（Ｄ１）→Ｍｍｎ（Ｄ２） 和ｇ：Ｍｎｍ （Ｄ１） →Ｍｎｍ （Ｄ２）满足ｆ（Ａ）＋ ＝ ｇ（Ａ＋ ）对于一切的Ａ∈Ｍｍ ｎ（Ｄ１）均成立,则称（ｆ, ｇ） 是一个保矩阵ＭＰ逆的共变算子对． 当ｍ ｉｎ（ｍ , ｎ）２时,本文刻划了所有这种共变算子对（ｆ, ｇ） 的结构．     

布尔矩阵广义逆A－ω，A－d，A－ω

设Ａ是布尔矩阵，而矩阵Ｇ满足ＡＧＡ＝Ａ．（１）如果对所有Ａｘ＝ｙ的向量ｘ，ｙ．有ω（Ｇｙ）≤ω（ｘ）（＊）称Ｇ是Ａ的一个极小权ｇ－逆，表示为Ａ－ω．（２）如果对所有向量ｘ，ｙ，有ｄ（ＡＧｙ，ｙ）≤ｄ（Ａｘ，ｙ）（＊＊）称Ｇ是Ａ的最小距离ｇ－逆，表示为Ａ－ｄ．（３）如果（＊）和（＊＊）都成立，就称Ｇ是极小权最小距离ｇ－逆，表示为Ａ－ωｄ．本文研究这三类广义逆矩阵的最大逆的存在性及表示式．主要结果如下：假定对于矩阵Ａ．Ａ－ω，Ａ－ｄ，Ａ－ωｄ分别存在，那么．（１）存在最大Ａ－ω，当且仅当Ａ中设有两个相同的非零列，且最大Ａ－ω为Ａω＝［ＩＣＡＴ］Ｃ．（２）最大Ａ－ｄ存在，且为Ａｄ＝［ＡＴＡＣＡＴ＋ＡＴ（ＪＡＴ）Ｃ］Ｃ．（３）存在最大Ａ－ωｄ，当且仅当Ａ的所有非零列向量线性独立，且最大Ａ－ωｄ为Ａωｄ＝［ＡＴＡｃＡＴ＋ＡＴ（ＪＡＴ）ｃ＋（ＡＴＪ）ｃＡＴ］Ｃ．其中Ｊ为全１矩阵     

奇异M─矩阵的图相容弱正则分裂

设Ａ是奇异Ｍ－矩阵，Ａ＝Ｍ－Ｎ是Ａ的图相容弱正则分裂．本文研究迭代矩阵Ｍ－１Ｎ的谱性质，得到与迭代矩阵的指数有关的一个定理：ｉｎｄ０（Ａ）＝ｉｎｄ１（Ｍ－１Ｎ）．它推广了Ｈ．Ｓｃｈｎｅｉｄｅｒ和作者的结果．     

‖B~（－1）A‖的估计和H矩阵的充分条件

‖Ｂ~（－１）Ａ‖的估计和Ｈ矩阵的充分条件黄廷祝，游兆永（电子科技大学数学系成都６１００５４）（西安交大数学所西安７１００４９）关键词：范数；Ｈ矩阵；迭代法；矩阵分解ＡＭＳ（１９引）主题分类：６５Ｆ１０；６５Ｆ１５；１５Ａ４８本文讨论ＩＢ－’Ａｌ一和?..     

奇异M—矩阵的图相容弱正则分裂

设Ａ是奇异Ｍ－矩阵，Ａ＝Ｍ－Ｎ是Ａ的图相容弱正则分裂。本文研究迭代矩阵Ｍ＾－１Ｎ的谱性质，得到与迭代矩阵的指数有关的一个定理：ｉｎｄ０（Ａ）＝ｉｎｄ１（Ｍ＾－１Ｎ）．它推广了Ｈ．Ｓｃｈｎｅｉｄｅｒ和作者的结果。     

误差估计中矩阵求逆条件数的最优性在Hilbert空间中的推广

本文利用Ｈｉｌｂｅｒｔ空间中可逆算子的极分解定理，将误差估计中矩阵求逆条件数的最优性在Ｈｉｌｂｅｒｔ空间中进行推广，证明了线性有界算子Ａ的求逆条件数Ｋ（Ａ）＝ＡＡ－１在求算子扰动逆（Ａ＋Ｅ）－１的相对误差界中的极小性质，指出了算子求逆条件数在误差估计中为仅与算子Ａ有关的最佳常数值．     

恰含d个非零对角元的本原矩阵的广义最大密度指数集

设Ａ是一个具有周期ｐ的ｎ×ｎ不可约布尔矩阵,文［１］定义了矩阵的广义最大密度指数ｈＡ（ｋ）令ＤＩＳｎ,ｄ（ｋ）＝｛ｈＡ（ｋ）｜ Ａ ＰＭｎ（ｄ）｝,其中ＰＭｎ（ｄ）是所有恰含ｄ个非零对角元的ｎ×ｎ本原矩阵的集合．本文证明了另外,我们定义矩阵Ａ的范数,用Ａ表示,为Ａ中１的个数,并且刻划了具有最小范数的极矩阵．     

关于正规Boole矩阵行空间的的基数

称Ｂｏｏｌｅ矩阵Ａ是正规是，是指Ａ的行秩与列秩相等。本文主要得到两个结果。第一，推广了Ｊ．Ｋｏｎｉｅｃｚｎｙ在Ｓｅｍｉｇｒｏｕｐ ｆＯＲＵＭ，ｖｏｌ．４４（１９９２）发表的论文Ｏｎ ｃａｒｄｉｎａｌｉｔｉｅｓ ｏｆ ｒｏｗ ｓｐａｃｅ ｏｆ Ｂｏｏｌｅａｎ ｍａｔｒｉｃｅｓ的重要结果。第二，若ｎ阶Ｂｏｏｌｅ矩阵的行空间基数大于２＾ｎ－１－２，则Ａ必是正规的。     

广义严格对角占优矩阵与非奇M矩阵的判定

１引言Ｍ矩阵是计算数学中应给极其广泛的矩阵类,它出现于经济价值模型矩阵和反网络系统分析的系数矩阵及解某类确定微分方程问题的数值解法中．由于Ｍ矩阵的重要性,讨论Ｍ矩阵及相关的广义对角占优矩阵的判定及性质有着十分重要的意义．本文则是在文［１］～［３］基础上,给出了广义严格对角占优矩阵与非奇Ｍ矩阵几则新的充分条件．拓广了文［１］～［３］的相关结果．２主要结果定义１设Ａ＝（ａｉｊ）,如果存在正对角阵Ｄ,使得ＡＤ为严格对角占优阵,则称Ａ为广义严格对角占优阵．定义２设Ａ＝,Ｍ（Ａ）＝（Ｍｉｊ）,其中,则称Ｓ…     

On Separation Index of Heegaard Splittings

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｃｏｎｃｅｐｔｏｆｒｅｄｕｃｉｂｌｅＨｅｅｇａａｒｄｓｐｌｉｔｉｎｇｓｗａｓｆｉｒｓｔｄｅｖｅｌｏｐｅｄｂｙＨａｋｅｎ［１］．Ｉｔｓｒｅｌａ－ｔｉｏｎｔｏｔｈｅｃｏｒｒｅｓｐｏｎｄｉｎｇ３－ｍａｎｉｆｏｌｄｓｃｏｎ...     

A note on nonnegative rank factorizations

A nonnegative weakly monotone matrix of rank r has a nonnegative rank factorization if and only if it possesses an rxr monomial submatrix.     

On some factorizations of two-parameter polynomial matrices

This paper is a logical continuation of the author's discussion about the solution of spectral problems for two-parameter polynomial matrices of general type. Various rank factorization algorithms are suggested, among them the so-called minimal factorization of a singular two-parameter polynomial matrix of degenerate rank into a product of some matrices whose ranks are equal to the rank of the original matrix. Spectral properties of these matrices are studied. The notion of minimal factorization is also extended to one-parameter polynomial and constant matrices. Bibliography: 13 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 219, 1994, pp. 94–116 Translated by V. N. Kublanovskaya.     

Q5‐factorization of λKn

Q_k is the simple graph whose vertices are the k‐tuples with entries in {0, 1} and edges are the pairs of k‐tuples that differ in exactly one position. In this paper, we proved that there exists a Q₅‐factorization of λK_n if and only if (a) n ≡ 0(mod 32) if λ ≡ 0(mod 5) and (b) n ≡ 96(mod 160) if λ ? 0(mod 5).     

Products of quasireflections and transvections over local rings

Let R be a commutative local ring and M a free R-module of rank n. The module M is endowed with a metric structure given by a sesquilinear form or by a quadratic form. We show, every isometry of M is a product of quasireflections or transvections. We determine the minimal number of factors needed in any factorization of if the path of is a subspace. For all other isometries we obtain only an upper bound.Research supported in part by NSERC Canada grant A7251To Helmut Karzel on his 60th birthday     

On some ranks of infinite groups

Abstract A group G has finite Hirsch-Zaicev rank r_hz(G) = r if G has an ascending series whose factors are either infinite cyclic or periodic and if the number of infinite cyclic factors is exactly r. The authors discuss groups with finite Hirsch-Zaicev rank and the connection between this and groups having finite section p-rank for some prime p, or p=0. Groups all of whose abelian subgroups are of bounded rank are also discussed. Keywords: p-rank, locally generalized radical group, Hirsch-Zaicev rank, torsion-free rank, rank Mathematics Subject Classification (2000): 20F19, 20E25, 20E15     

Test elements for monomorphisms of free lie algebras and lie superalgebras †

A test criterion for an endomorphism φ of the free Lie (super) algebra L of finite rank to be an automorphism is obtained: φ is an automorphism of L if and only if for an element u ∈ L with the maximal rank the element φ(u) belongs to the orbit of u with respect to the automorphism group of L. In particular, test elements for monomorphisms of L are exactly the elements of the maximal rank     

Connected components of the category of elementary abelian p-subgroups

We determine the maximal number of conjugacy classes of maximal elementary abelian subgroups of rank 2 in a finite p-group G, for an odd prime p. Namely, it is p if G has rank at least 3 and it is p+1 if G has rank 2. More precisely, if G has rank 2, there are exactly 1,2,p+1, or possibly 3 classes for some 3-groups of maximal nilpotency class.     

有限生成亚投射模范畴

对一个QF环R,本文证明:其投射左R模范畴是因式分解范畴当且仅当gl.dim R≤1．进一步,若 P(_RR)＝P(R_R)＝0,则其通过左模而得到的亚 Crothendieck群与其通过右模而得到的亚Grothendieck群在同构意义下是一样的．还证明了有限生成亚投射左R－模范畴不仅是一个因式分解范畴而且是一个带积的具有小的骨架子范畴的范畴．     

On large half-factorial sets in elementary<Emphasis Type="Italic">p</Emphasis>-groups: Maximal cardinality and structural characterization

Half-factoriality is a central concept in the theory of non-unique factorization, with applications for instance in algebraic number theory. A subsetG ₀ of an abelian group is called half-factorial if the block monoid overG ₀, which is the monoid of all zero-sum sequences of elements ofG ₀, is a half-factorial monoid. In this paper we study half-factorial sets with large cardinality in elementaryp-groups. First, we determine the maximal cardinality of such half-factorial sets, and generalize a result which has been only known for groups of even rank. Second, we characterize the structure of all half-factorial sets with large cardinality (in a sense made precise in the paper). Both results have a direct application in the study of some counting functions related to factorization properties of algebraic integers. This work was supported by the Austrian Science Fund FWF (Project P16770-N12) and by the Austrian-French Program ‘Amadeus 2003–2004’.