Generic Idempotent Modules for a Finite Group

Let G be a finite group and k an algebraically closed field of characteristic p. Let F _U be the Rickard idempotent k G-module corresponding to the set U of subvarieties of the cohomology variety V _G which are not irreducible components. We show that F _U is a finite sum of generic modules corresponding to the irreducible components of V _G . In this context, a generic module is an indecomposable module of infinite length over k G but finite length as a module over its endomorphism ring.     

Modules Which Satisfy the Radical Formula

Let be a commutative ring. Then an -module M satisfies the radical formula when is a direct sum of a submodule M ₁ which satisfies the radical formula and a semi-artinian submodule M ₂.     

挠理论中的相对内射模

For a hereditary torsion theory T,this paper mainly discuss properties of A-τ- injective modules,where A is a fixed left R-module.It is proved that if M is an A-τ-injective, B is a submodule of A,then 1)M is A/B-τ-injective;2)M is B-τ-injective when B isτ- dense in A.Furthermore,we show that if A_1,A_2,…,A_n are relatively injective modules, then A_1⊕A_2⊕…⊕A_n is self-τ-injective if and only if A_i is self-τ-injective for each i.     

The Idempotent Manifold in a Clifford Algebra

The idempotent sets in sufficiently sophisticated algebras form manifolds and Hausdorff spaces. In this paper it is shown how the idempotents in a real Clifford algebra Cl_p,q can be calculated by nilpotents and reflections. Minimal sets of nilpotents are given and generating relations are defined. It is shown that the manifold thus constructed is complete. Every idempotent in the manifold can be calculated in the way proposed here, namely by a nilpotent multinomial form.     

幂等剩余格

研究一种特殊的刺余格--幂等刺余格,证明满足幂等性的一般刺余格必是可换剩余格,即不存在非可换的幂等剩余格.讨论幂等剩余格的基本性质以及与各类特殊剩余格之间的关系.在一般剩余格中引入psG-滤子的概念,给出其一组等价条件,并借助psG-滤子刻画幂等刺余格的特征.     

Globals of Idempotent Semigroups

If S is a semigroup, the global (or the power semigroup) of S is the set P(S) of all nonempty subsets of S equipped with a naturally defined multiplication. A class K of semigroups is globally determined if any two semigroups of K with isomorphic globals are themselves isomorphic. We study properties of globals of idempotent semigroups and show, in particular, that the class of normal bands is globally determined.     

Higher Level Orderings on Modules

The aim of this paper is to investigate higher level orderings on modules over commutative rings. On the basis of the theory of higher level orderings on fields and commutative rings, some results involving existence of higher level orderings are generalized to the category of modules over commutative rings. Moreover, a strict intersection theorem for higher level orderings on modules is established.     

三幂等矩阵的一些性质

重点探索了三幂等矩阵的性质.主要从矩阵乘积、线性变换和矩阵的秩等角度出发,将幂等矩阵的性质向三幂等矩阵推广,对三幂等矩阵的性质进行探究,得到了15个相关结论,并给出部分性质的详细推导过程.     

具有幂等自反自同态的环

通过引入环的幂等自反自同态α的概念,研究幂等自反α-环,它是幂等自反环概念的拓广.给出幂等自反α-环的一些特征和扩张性质,推广了已有的一些相关结果.     

Idempotent probability measures on ultrametric spaces

Following the construction due to Hartog and Vink we introduce a metric on the set of idempotent probability measures (Maslov measures) defined on an ultrametric space. This construction determines a functor on the category of ultrametric spaces and nonexpanding maps. We prove that this functor is the functorial part of a monad on this category. This monad turns out to contain the hyperspace monad.     

Idempotent completions of operator partial matrices

Necessary and sufficient conditions are obtained for operator partial 2 × 2 matrices to have an idempotent completion, and all such completions are parametrically represented. Project supported by National Natural Science Foundation of China and Provincial Natural Science Foundation of Shanxi     

On Fully Idempotent Homomorphisms of Abelian Groups

Siberian Mathematical Journal - We provide some examples of irregular fully idempotent homomorphisms and study the pairs of abelian groups A and B for which the homomorphism group Hom(A, B) is...     

幂等右侧Quantale上的幂零矩阵

讨论幂等右侧Quantale上的幂零矩阵的若干性质，给出了幂等右侧Quantale上的矩阵为幂零矩阵的充要条件，得到了幂零矩阵的幂零指数的刻画定理。     

On finiteness of multiplication modules

Our main aim in this note, is a further generalization of a result due to D. D. Anderson, i.e., it is shown that if R is a commutative ring, and M a multiplication R-module, such that every prime ideal minimal over Ann (M) is finitely generated, then M contains only a finite number of minimal prime submodules. This immediately yields that if P is a projective ideal of R, such that every prime ideal minimal over Ann (P) is finitely generated, then P is finitely generated. Furthermore, it is established that if M is a multiplication R-module in which every minimal prime submodule is finitely generated, then R contains only a finite number of prime ideals minimal over Ann (M).      

On Divisible and Torsionfree Modules

A ring R is called left P-coherent in case each principal left ideal of R is finitely presented. A left R-module M (resp. right R-module N) is called D-injective (resp. D-flat) if Ext¹(G, M) = 0 (resp. Tor₁(N, G) = 0) for every divisible left R-module G. It is shown that every left R-module over a left P-coherent ring R has a divisible cover; a left R-module M is D-injective if and only if M is the kernel of a divisible precover A → B with A injective; a finitely presented right R-module L over a left P-coherent ring R is D-flat if and only if L is the cokernel of a torsionfree preenvelope K → F with F flat. We also study the divisible and torsionfree dimensions of modules and rings. As applications, some new characterizations of von Neumann regular rings and PP rings are given.     

关于幂等阵的相似与线性组合

证明了数域上两个同阶幂等阵相似的充要条件是它们有相同的秩;给出了幂等阵的相似标准型;讨论了两个幂等阵的线性组合仍是幂等阵的充要条件.