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61.
Alexander Schmeding 《代数通讯》2013,41(1):228-237
In this paper we reconsider a classical theorem by Bican and El Bashir, which guarantees the existence of non-trivial relatively pure submodules in a module category over a ring with unit. Our aim is to generalize the theorem to module categories over rings with several objects. As an application, we then consider the special case of α-pure objects in such module categories. 相似文献
62.
Let R and S be two rings. Each category equivalence between a torsion class of left (right) R-modules and a torsion-free class of left (right) S-modules is represented by a left (right) quasi-tilting triple. Suppose we have a pair of equivalences T ? Y and X F between the torsion class T of R-modules and the torsion-free class Y of S-modules and between the torsion class X of S-modules and the torsion-free class F of R-modules. Denote by (R, V, S) and (S, U, R) the quasi-tilting triples representing these equivalences. We say that (R, V, S) and (S, U, R) are complementary if T, F) and X, Y) are torsion theories in R-Mod and S-Mod, respectively. We find necessary and sufficient conditions on the bimodules RVS and SUR to have the complementarity of (R, V, S) and (S, U, R). 相似文献
63.
For a finite free and projective EI category, we prove that Gorenstein-projective modules over its category algebra are closed under the tensor product if and only if each morphism in the given category is a monomorphism. 相似文献
64.
该文研究范畴中态射α关于对称态射β和γ的加权Moore Penrose逆αβ,γ+ ,分别给出了一般态射、有满单分解态射与有核(上核)态射的αβ,γ+ 存在的充要条件及其相应的表达式. 相似文献
65.
66.
We prove that operator algebras that have enough projections are completely determined by those projections, their symmetries, and the action of the latter on the former. This includes all von Neumann algebras and all AW*-algebras. We introduce active lattices, which are formed from these three ingredients. More generally, we prove that the category of AW*-algebras is equivalent to a full subcategory of active lattices. Crucial ingredients are an equivalence between the category of piecewise AW*-algebras and that of piecewise complete Boolean algebras, and a refinement of the piecewise algebra structure of an AW*-algebra that enables recovering its total structure. 相似文献
67.
Shigeki Matsutani 《Applied mathematics and computation》2010,217(2):568-579
The CIP-method is a numerical computational method in the computational fluid dynamics discovered by Takewaki, Nishiguchi and Yabe [H. Takewaki, A. Nishiguchi, T. Yabe, The cubic-interpolated pseudo-particle (CIP) method for solving hyperbolic-type equations, J. Comput. Phys. 61 (1985) 261-268], which shows nice properties as a numerical computational method but it is known that its mathematical essentials have not been revealed well. In this article we investigate the CIP-method from an algebraic viewpoint. Then it is shown that the CIP-method is described well in terms of the sheaf theory. 相似文献
68.
Adam J. Prze
dziecki 《Journal of Algebra》2008,320(12):4270-4280
We construct examples of localizations in the category of groups which take the Mathieu group M11 to groups of arbitrarily large cardinality which are “abelian up to finitely many generators.” The paper is part of a broader study on the group theoretic properties which are or are not preserved by localizations. 相似文献
69.
Selçuk Demir 《Geometriae Dedicata》2006,120(1):99-109
This is the continuation of our previous work (Demir, Geom. Dedicata 105, 189–207, 2004). In this paper, we study extensions between admissible representations of the isometry groups of regular trees. We use the results of Demir, (Geom. Dedicata 105, 189–207, 2004) to show, following Schneider and Stuhler (J. Reine. Angew. Math. 436, 19–32, 1993) in the p-adic case, that extensions between admissible representations of G are finite-dimensional. 相似文献
70.
该文研究预加法范畴中态射的广义逆, 利用幂等态射给出了态射广义逆存在的充要条件及其表达式. 得到预加法范畴中态射的柱心 幂零分解存在的充要条件, 并给出了分解的方法 相似文献