函子范畴上加性函子的一个表示

研究函子范畴ModC上加性函子的表示,把一个Abel群作成范畴ModC上的一个左C-模,构造出一个Hom函子和一个函子态射,证明了从函子范畴ModC到范畴Ab的任意变和为积的反变左正合可加函子都与某个Hom函子自然等价.所得结论在函子范畴上,推广了Watts定理.     

Dyadic Mappings and Dyadic Superparacompact Topological Groups

We introduce the notion of a dyadic superparacompactum which generalizes the classical notion of a dyadic bicompactum and give an analog of V. I. Kuz’minov and L. N. Ivanovskii’s Theorem on dyadicity of the space of a bicompact topological group for superparacompact groups. Moreover, we generalize L. S. Pontryagin’s Theorem on existence of an open bicompact subgroup in each neighborhood of unity of a locally bicompact totally disconnected topological group.Original Russian Text Copyright © 2005 Musaev D. K.__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 851–859, July–August, 2005.     

Local Morphisms and Modules with a Semilocal Endomorphism Ring

We study local morphisms in the setting of general noncommutative rings. In particular, we apply local morphisms to study endomorphism rings of modules. We use our constructions to determine classes of modules with semilocal endomorphism rings. For instance, we prove that every finitely presented right module over a semilocal ring has a semilocal endomorphism ring.Alberto Facchini was partially supported by Gruppo Nazionale Strutture Algebriche e Geometriche e loro Applicazioni of Istituto Nazionale di Alta Matematica, Italy, and by Università di Padova (Progetto di Ateneo CDPA048343 “Decomposition and tilting theory in modules, derived and cluster categories”).Dolors Herbera was partially supported by the DGI and the European Regional Development Fund, jointly, through Project BFM2002-01390, and by the Comissionat per Universitats i Recerca of the Generalitat de Catalunya.     

Abel范畴中线性态射方程的公共解及一类同解方程

给出了Ａｂｅｌ范畴中形如ψχψ＝τ的态射方程有解的充要条件以及线性态射方程ψχ＝τ１，χψ＝τ２有公共解的条件，并讨论了Ａｂｅｌ范畴中的一类同解方程。     

关于态射的加权Moore-Penrose逆

研究了范畴中态射 f关于态射β和γ的加权 Moore-Penrose逆 fβ,γ+,分别给出了一般态射、有满单分解态射与有核 (上核 )的 fβ,γ+存在的充要条件及其相应的表达式 ,推广了 f关于对称态射β和γ的加权Moore-Penrose逆的相应结果 .     

Tensor products of Hilbert space effect algebras

A definition of a tensor product in the category of Hilbert space effect algebras is introduced such that the tensor product reflects as much as possible of the physically important properties of the components. It is shown that in the complex case, there are two candidates to the tensor product, which are not equivalent. The situation is similar to the tensor product in the category of projection lattices, but also the two dimensional case is included. The case of tensor product of two classical systems is also investigated.     

预加法范畴中态射集星型序的刻划

本文给出了预加法范畴中态射集左（右）星序，星序的显公式刻划，证得了素性，正性预加法范畴中态射集星型序的某些刻划，把Ｈａｒｔｗｉｇ，Ｓｔｙａｎ，Ｍｉｔｒａ，Ｂａｋｓａｌａｒｙ关于复矩阵星型序刻划的有关结果推广到这两类范畴中。     

The Groups LS and Morphisms of Quadratic Extensions

For a morphism of quadratic extensions of antistructures, groups similar to the groups of obstructions to splitting along one-sided submanifolds are defined. These groups are a natural generalization of the splitting obstruction groups. The results obtained open additional possibilities for constructing groups and natural maps in L-theory.     

Openness with Respect to a Closure Operator

We study the notions of closed, open, initial and final morphism with respect to a closure operator and show that they have a perfectly symmetric pullback behaviour. We also investigate their interaction with closed and with open subobjects and the impact of the existence of suitably defined complements of subobjects.