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1.
Miodrag-Cristian Iovanov 《Applied Categorical Structures》2006,14(5-6):599-604
In this note we give a new and elementary proof of a result of Năstăsescu and Torrecillas (J. Algebra, 281:144–149, 2004) stating that a coalgebra C is finite dimensional if and only if the rational part of any right module M over the dual algebra is a direct summand in M (the splitting problem for coalgebras).
Research supported by a CNCSIS BD-type grant, and by the bilateral project BWS04/04 “New Techniques in Hopf Algebra Theory
and Graded Ring Theory” of the Flemish and Romanian governments. 相似文献
2.
郑乃峰 《纯粹数学与应用数学》2013,(1):11-18
设H为弱Hopf代数,C为弱右H-模余代数,令C=C/C·ker L.利用Smash余积来研究弱模余代数上的结构定理,并给出了C与C×H作为余代数同构的条件. 相似文献
3.
By further generalizing the skew-symmetric triangular splitting iteration method studied by Krukier, Chikina and Belokon (Applied Numerical Mathematics, 41 (2002), pp. 89–105), in this paper, we present a new iteration scheme, called the modified skew-Hermitian triangular splitting iteration method, for solving the strongly non-Hermitian systems of linear equations with positive definite coefficient matrices. We discuss the convergence property and the optimal parameters of this new method in depth. Moreover, when it is applied to precondition the Krylov subspace methods like GMRES, the preconditioning property of the modified skew-Hermitian triangular splitting iteration is analyzed in detail. Numerical results show that, as both solver and preconditioner, the modified skew-Hermitian triangular splitting iteration method is very effective for solving large sparse positive definite systems of linear equations of strong skew-Hermitian parts. 相似文献
4.
Thomas Hüttemann 《代数通讯》2017,45(7):2757-2774
We investigate modules over “systematic” rings. Such rings are “almost graded” and have appeared under various names in the literature; they are special cases of the G-systems of Grzeszczuk. We analyse their K-theory in the presence of conditions on the support, and explain how this generalises and unifies calculations of graded and filtered K-theory scattered in the literature. Our treatment makes systematic use of the formalism of idempotent completion and a theory of triangular objects in additive categories, leading to elementary and transparent proofs throughout. 相似文献
5.
6.
杜先能 《数学年刊A辑(中文版)》2006,(2)
本文研究形式三角矩阵环 R 的若干新性质,讨论 R-模的伪投射性,给出了形式三角矩阵环 R 是 V-环或半 V-环的充要条件.同时,给出了 R 是 PS-环的条件. 相似文献
7.
Bienvenido Cuartero José E. Galé Arkadii M. Slinko 《Proceedings of the American Mathematical Society》1997,125(7):1945-1952
It is proved that if the dual Lie algebra of a Lie coalgebra is algebraic, then it is algebraic of bounded degree. This result is an analog of the D.Radford's result for associative coalgebras.
8.
We study Dorroh extensions of algebras and Dorroh extensions of coalgebras. Their structures are described. Some properties of these extensions are presented. We also introduce the finite duals of algebras and modules which are not necessarily unital. Using these finite duals, we determine the dual relations between the two kinds of extensions. 相似文献
9.
Ladislav Bican 《代数通讯》2013,41(11):4098-4103
It is well-known (see [13]) that a hereditary torsion theory τ for the category R-mod is noetherian if and only if the class of all τ-torsionfree τ-injective modules is closed under arbitrary direct sums. So, it is natural to investigate the hereditary torsion theories having the property that the class of all τ-torsionfree injective modules is closed under arbitrary direct sums, which are called ?-noetherian. These torsion theories have been studied by Teply in [16]. In the second part of this note we shall study the weakly exact hereditary torsion theories, which generalize the exact one's. 相似文献
10.
文章对$3\times 3$阶三角矩阵环$$\Gamma = \left(\begin{array}{ccc}T & 0 & 0 \\M & U & 0\\{N \otimes _U M} & N & V \\\end{array}\right)$$上的模作了研究,其中T,U,V均是环, M,N分别是U-T, V-U双模.通过用一个五元组$(A,B,C;f,g)$来描述一个左$\Gamma$-模 (其中$A \in \mod T, B\in {\rm mod} U, C \in {\rm mod} V$, $f:M \otimes _T A \to B \in {\rm mod} U, g:N \otimes _U B \to C \in {\rm mod} V$), 文章分别刻画了$\Gamma$上的一致模、空的模、有限嵌入模,并且确定了${ }_\Gamma (A \oplus B \oplus C)$的根和基座. 相似文献
11.
我们研究了形式三角矩阵环上模的Gorenstein(半遗传)遗传性,有限表现性和FP-内射性.给出了形式三角矩阵环是Gorenstein(半遗传)遗传的充要条件,并得出了形式三角矩阵环是n-FC环的充分条件. 相似文献
12.
本文通过函子T=-ARnA讨论了倾斜A 模与倾斜RnA 模的重要联系,推广了[1]的主要结果;讨论了倾斜RnA 模TX与倾斜A 模导出的挠理论在相同性和分裂性等方面的关系. 相似文献
13.
Let M be a right R-module,
the class of all M-small modules, and P a projective cover of M in
[M]. We consider the torsion theories
= (
),
= (
), and
= (
) in
[M], where
is the torsion theory generated by
is the torsion theory cogenerated by
, and
is the dual Lambek torsion theory. We study some conditions for
to be cohereditary, stable, or split, and prove that Rej(M,
) = M
=
(=
=
)
=
GenM(P)
.2000 Mathematics Subject Classification: 16S90 相似文献
14.
15.
Liang-yun Zhang 《Siberian Mathematical Journal》2006,47(4):767-778
Given an (H,R)-Lie coalgebra Γ, we construct (H,R T )-Lie coalgebra ΓT through a right cocycle T, where (H,R) is a triangular Hopf algebra, and prove that there exists a bijection between the set of (H,R)-Lie coalgebras and the set of ordinary Lie coalgebras. We also show that if (L, [, ], Δ, R) is an (H,R)-Lie bialgebra of an ordinary Lie algebra then (L T , [, ], ΔT, R T ) is an (H,R T )-Lie bialgebra of an ordinary Lie algebra. 相似文献
16.
针对时间权重与属性权重完全未知的三角模糊多属性决策问题,基于前景理论和MULTIMOORA提出一种新的决策方法。首先,建立备选方案在不同时段的三角模糊前景决策矩阵,根据时间度及不同时段内备选方案前景值的差异构建时间权重优化模型,并运用最大偏差法的基本思想获得属性权重。其次,基于三角模糊数提出一种新的MULTIMOORA扩展形式,并结合占优理论对备选方案进行比选。最后,通过实例证明了所提方法是可行的,也是有效的。 相似文献
17.
The aim of this paper is mainly to build a new representation-theoretic realization of finite root systems through the so-called Frobenius-type triangular matrix algebras by the method of reflection functors over any field. Finally, we give an analog of APR-tilting module for this class of algebras. The major conclusions contains the known results as special cases, e.g., that for path algebras over an algebraically closed field and for path algebras with relations from symmetrizable cartan matrices. Meanwhile, it means the corresponding results for some other important classes of algebras, that is, the path algebras of quivers over Frobenius algebras and the generalized path algebras endowed by Frobenius algebras at vertices. 相似文献
18.
Amnon Yekutieli 《代数通讯》2013,41(11):4221-4245
Let A be a noetherian commutative ring, and let 𝔞 be an ideal in A. We study questions of flatness and 𝔞-adic completeness for infinitely generated A-modules. This is done using the notions of decaying function and 𝔞-adically free A-module. 相似文献
19.
Let R be a commutative ring. An Azumaya coring consists of a couple
, with S a faithfully flat commutative R-algebra, and an S-coring
satisfying certain properties. If S is faithfully projective, then the dual of
is an Azumaya algebra. Equivalence classes of Azumaya corings form an abelian group, called the Brauer group of Azumaya corings.
This group is canonically isomorphic to the second flat cohomology group. We also give algebraic interpretations of the second
Amitsur cohomology group and the first Villamayor–Zelinsky cohomology group in terms of corings. 相似文献
20.
Semra Doğruöz 《Czechoslovak Mathematical Journal》2008,58(2):381-393
An R-module M is said to be an extending module if every closed submodule of M is a direct summand. In this paper we introduce and investigate the concept of a type 2 τ-extending module, where τ is a hereditary torsion theory on Mod-R. An R-module M is called type 2 τ-extending if every type 2 τ-closed submodule of M is a direct summand of M. If τ
I
is the torsion theory on Mod-R corresponding to an idempotent ideal I of R and M is a type 2 τ
I
-extending R-module, then the question of whether or not M/MI is an extending R/I-module is investigated. In particular, for the Goldie torsion theory τ
G
we give an example of a module that is type 2 τ
G
-extending but not extending. 相似文献