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1.
Let W be an injective unilateral weighted shift, and let W(n) be the orthogonal direct sum of n copies of W. In this paper, we prove that, if the commutant of W is strictly cyclic, then W(n) has a unique (SI) decomposition with respect to similarity for every natural number n. 相似文献
2.
岳华 《数学的实践与认识》2003,33(6):96-104
本文证明了可分无穷维 Hilbert空间上每个有界线性算子均可写成两个强不可约算子之和 .这回答了文献 [9]中提出一个公开问题 相似文献
3.
In the Gorenstein homological theory, Gorenstein projective and Gorenstein injective dimensions play an important and fundamental role. In this paper, we aim at studying the closely related strongly Gorenstein flat and Gorenstein FP-injective dimensions, and show that some characterizations similar to Gorenstein homological dimensions hold for these two dimensions. 相似文献
4.
在有限维空间的矩阵理论中,著名的约当标准型定理充分揭示了矩阵的内在结构.在这篇综述中,我们给出复可分的无穷维希尔伯特空间上类似的约当标准型定理.同时也展示了该理论在其它数学分支中的应用。 相似文献
5.
Sang Bum Lee 《代数通讯》2013,41(3):1232-1240
Strongly flat modules were introduced by Bazzoni–Salce [3] and used to characterize almost perfect domains. Here we wish to study strongly flat modules, more generally, over Matlis domains; these are integral domains R such that the field of quotients Q has projective dimension 1. In Section 2, criteria are proved for strong flatness. We also prove that over arbitrary domains, strongly flat submodules of projective modules are projective (Theorem 3.2), in particular, strongly flat ideals are projective (Corollary 3.4) and use these results to show that the strongly flat dimension (which makes sense over Matlis domains) coincides with the projective dimension whenever it is > 1. 相似文献
6.
We introduce the dual notion to soc-injectivity, namely rad-projective and strongly rad-projective modules. Several interesting results and applications on the new notion are obtained. 相似文献
7.
Chunlan Jiang Shunhua Sun Zongyao Wang 《Transactions of the American Mathematical Society》1997,349(1):217-233
It is shown that given an essentially normal operator with connected spectrum, there exists a compact operator such that is strongly irreducible.
8.
首先,利用量子群Uq (D4)的已知的Grobner-Shirshov基和Chibrikov的双自由模方法来计算量子群Uq(D4)上不可约模Vq(λ)的一个Grobner-Shirshov对,然后在Uq(D4)的适当形式U'q(D4)中取q=1得到D4型单李代数的泛包络代数U(D4)上不可约模V(λ)的一个Grobner-Shirshov对. 相似文献
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10.
Majid M. Ali 《代数通讯》2013,41(12):4620-4642
All rings are commutative with identity, and all modules are unital. The purpose of this article is to investigate multiplication von Neumann regular modules. For this reason we introduce the concept of nilpotent submodules generalizing nilpotent ideals and then prove that a faithful multiplication module is von Neumann regular if and only if it has no nonzero nilpotent elements and its Krull dimension is zero. We also give a new characterization for the radical of a submodule of a multiplication module and show in particular that the radical of any submodule of a Noetherian multiplication module is a finite intersection of prime submodules. 相似文献
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12.
Zenghui Gao 《代数通讯》2013,41(8):3035-3044
This article continues to investigate a particular case of Gorenstein FP-injective modules, called strongly Gorenstein FP-injective modules. Some examples are given to show that strongly Gorenstein FP-injective modules lie strictly between FP-injective modules and Gorenstein FP-injective modules. Various results are developed, many extending known results in [1]. We also characterize FC rings in terms of strongly Gorenstein FP-injective, projective, and flat modules. 相似文献
13.
In this article, we introduce the dual notion of content (i.e., cocontent) modules over commutative rings and investigate some basic properties of this class of modules. 相似文献
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15.
A. R. Naghipour 《代数通讯》2013,41(7):2193-2199
Let R be a commutative ring with identity. For an R-module M, the notion of strongly prime submodule of M is defined. It is shown that this notion of prime submodule inherits most of the essential properties of the usual notion of prime ideal. In particular, the Generalized Principal Ideal Theorem is extended to modules. 相似文献
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17.
Prime Submodules and Flat Modules 总被引:2,自引:0,他引:2
A. AZIZI 《数学学报(英文版)》2007,23(1):147-152
In this paper, some characterizations of prime submodules in flat modules and, particularly, in free modules are given. Furthermore, the height of prime submodules and some saturated chain of prime submodules are also given. 相似文献
18.
This paper firstly discusses the existence of strongly irreducible operators on Banach spaces. It shows that there exist strongly
irreducible operators on Banach spaces with w*-separable dual. It also gives some properties of strongly irreducible operators on Banach spaces. In particular, if T is a strongly irreducible operator on an infinite-dimensional Banach space, then T is not of finite rank and T is not an algebraic operator. On Banach spaces with subsymmetric bases, including infinite-dimensional separable Hilbert
spaces, it shows that quasisimilarity does not preserve strong irreducibility. In addition, we show that the strong irreducibility
of an operator does not imply the strong irreducibility of its conjugate operator, which is not the same as the property in
Hilbert spaces. 相似文献
19.
M. Ghirati 《代数通讯》2013,41(2):564-580
The submodules with the property of the title (N ? M is strongly essential in M if ∏ I N is essential in ∏ I M for any index set I) are introduced and fully investigated. It is shown that for each submodule N of M there exists a subset T ? M such that N + T is strongly essential submodule of M and (N:T) = Ann(T), T ∩ N = 0. Basic properties of these objects and several examples are given and the counterparts of the related concepts to essential submodules are also introduced and studied. It is shown that each maximal left ideal of a left fully bounded ring is either a summand or strongly essential. Rings over which no module has a proper strongly essential submodule are characterized. It is also shown that the left Loewy rings are the only rings over which the essential submodules and strongly essential submodules of any left module coincide. Finally, a new characterization of left FBN rings is observed. 相似文献