Contact代数K(m,n)的不可约模的结构

利用广义限制李代数的概念和性质,研究Contact代数K(m,n)的不可约表示,给出了特征标高度大于等于2且小于p-3的不可约K(m,n)-模的结构.     

Commutative ideal theory without finiteness conditions: Completely irreducible ideals

An ideal of a ring is completely irreducible if it is not the intersection of any set of proper overideals. We investigate the structure of completely irrreducible ideals in a commutative ring without finiteness conditions. It is known that every ideal of a ring is an intersection of completely irreducible ideals. We characterize in several ways those ideals that admit a representation as an irredundant intersection of completely irreducible ideals, and we study the question of uniqueness of such representations. We characterize those commutative rings in which every ideal is an irredundant intersection of completely irreducible ideals.

     

常曲率流形中具平行李奇曲率的超曲面

设f:M~n→M~(n+1)(c)为具平行李奇曲率的黎曼流形到常曲率流形的等距浸入,本文给出了该超曲面的分类。另外,若M~n还是极小超曲面,本文也给出了该超曲面的分类,推广了Lawson的有关结果。     

The structure of irreducible matrix groups with submultiplicative spectrum

We describe the structure of irreducible matrix groups with submultiplicative spectrum. Since all such groups are nilpotent, the study is focused on p-groups. We obtain a block-monomial structure of matrices in irreducible p-groups and build polycyclic series arising from that structure. We give an upper bound to the exponent of these groups. We determine all minimal irreducible groups of p× p matrices with submultiplicative spectrum and discuss the case of p²× p² matrices if p is an odd prime.     

D_（6h）~1结构空间群C－G系数的计算

在晶体拉曼散射张量的计算中，晶体空间群的Ｃ－Ｇ系数具有重要作用，本文利用本征函数法~［１］，计算了一大类光学材料的结构空间群的Ｃ－Ｇ系数，同时给出波矢选择定则和Ｃ－Ｇ序列。     

Heart of Irreducible Morphisms of Bounded Complexes

In [9 Giraldo , H. , Merklen , H. ( 2009 ). Irreducible morphisms of categories of complexes . Journal of Algebra 321 : 2716 – 2736 .[Crossref], [Web of Science ®] , [Google Scholar]] Giraldo and Merklen studied irreducible morphisms in the categories 𝒞(𝒜) and D^?(Λ), where 𝒞(𝒜) is the category of complexes over an abelian Krull–Schmidt category 𝒜 and D^?(Λ) is the derived category of the bounded above complexes of finite generate left modules, over an Artin algebra Λ. In this work, we continue the study of irreducible morphism having one finite irreducible truncation.     

Null ideals and spanning ranks of matrices,II

Suppose R is an integral domain and A ∈ M _{n × n}(R) \{O}. If D is a spanning rank partner of A, then precisely one of the following three relationships holds: N _A = N _D N _A = XN _D or XN _A = N _D. Here X is an indeterminate and N _A(N _D) denotes the null ideal of A(D) in R[X]. There are easy examples of A and D for which N _A = N _D and N _A = XN _D. In this paper, we give an example where XN _A = N _D. We give sharper versions of the theorem for n ≤ 4.     

A Character Theoretic Condition for F(G) > 1

ABSTRACT

If G is a nontrivial finite group with the property that χ (1) ² divides bi| G | for all irreducible (complex) characters χ , then G has a nontrivial normal abelian subgroup.

     

On Generators and Representations of the Sporadic Simple Groups

In this paper we determine the irreducible projective representations of sporadic simple groups over an arbitrary algebraically closed field F, whose image contains an almost cyclic matrix of prime-power order. A matrix M is called cyclic if its characteristic and minimum polynomials coincide, and we call M almost cyclic if, for a suitable α ∈F, M is similar to diag(α·Id _h , M ₁), where M ₁ is cyclic and 0 ≤ h ≤ n. The paper also contains results on the generation of sporadic simple groups by minimal sets of conjugate elements.