共查询到20条相似文献,搜索用时 31 毫秒
1.
Motivated by [2] and [6], we introduce a generalization of extending (CS) modules by using the concept of τ-large submodule which was defined in [9]. We give some properties of this class of modules and study their relationship with
the familiar concepts of τ-closed, τ-complement submodules and the other generalization of extending modules (τ-complemented, τ-CS, s−τ-CS modules). We are also interested in determining when a τ-divisible module is τ-extending. For a τ-extending module M with C3, we obtain a decomposition theorem that there is a submodule K of M such that M = t(M) ? KM = \tau (M)\,\oplus\,K and K is τ (M)-injective. We also treat when a direct sum of τ-extending modules is τ-extending. 相似文献
2.
IfR is a right noetherian ring, the decomposition of an injective module, as a direct sum of uniform submodules, is well known.
Also, this property characterises this kind of ring. M. L. Teply obtains this result for torsion-free injective modules. The
decomposition of injective modules relative to a torsion theory has been studied by S. Mohamed, S. Singh, K. Masaike and T.
Horigone. In this paper our aim is to determine those rings satisfying that every torsion-freeτ-injective module is a direct sum ofτ-uniformτ-injective submodules and also to determine those rings with the same property for everyτ-injective module. 相似文献
3.
《Quaestiones Mathematicae》2013,36(6):789-792
AbstractIn this note, we provide a generalization of a well-known result of module theory which states that two injective modules are isomorphic when they are isomorphic to submodules of each other. More precisely, we show here that two RD-injective (respectively, pure-injective) modules over an integral domain are isomorphic if they are isomorphic to relatively divisible (respectively, pure) sub- modules of each other. 相似文献
4.
《Quaestiones Mathematicae》2013,36(8):1125-1139
AbstractIn this paper, we introduce a concept of a dual F-Baer module M where F is the fully invariant submodule of M, by this means we deal with generating dual Baer modules. We investigate direct sums of dual F -Baer modules M by exerting the notion of relatively dual F-Baer modules. We also obtain applications of dual F-Baer modules to rings and the preradical Z*(·). 相似文献
5.
A module M is called strongly FP-injective if Exti(P,M) = 0 for any finitely presented module P and all i≥1. (Pre)envelopes and (pre)covers by strongly FP-injective modules are studied. We also use these modules to characterize coherent rings. An example is given to show that (strongly) FP-injective (pre)covers may fail to be exist in general. We also give an example of a module that is FP-injective but not strongly FP-injective. 相似文献
6.
Kenji Nishida 《Algebras and Representation Theory》2006,9(1):13-31
We generalize results of Foxby concerning a commutative Nötherian ring to a certain noncommutative Nötherian algebra Λ over a commutative Gorenstein complete local ring. We assume that Λ is a Cohen–Macaulay isolated singularity having a dualizing module. Then the same method as in the commutative cases works and we obtain a category equivalence between two subcategories of mod Λ, one of which includes all finitely generated modules of finite Gorenstein dimension. We give examples of such algebras which are not Gorenstien; orders related to almost Bass orders and some k-Gorenstein algebras for an integer k.Presented by I. Reiten
★The author is supported by Grant-in-Aid for Scientific Researches B(1) No. 14340007 in Japan. 相似文献
7.
8.
We unify the cancellation property of rings with stable range one and the principal ideal domain by introducing a new notion
which is called “cancellable range”. It is proved that if a ring R has cancellable range n for some positive integer n, then for any n-generated module B and any module
implies B ≅ C; if R is a Noetherian ring and R has cancellable range n for any n ≧ 1, then R has the cancellation property.
Received: 16 November 2004 相似文献
9.
M. Zayed 《Archiv der Mathematik》2002,78(5):345-349
In this paper, the notions of f-injective and f*-injective modules are introduced. Elementary properties of these modules are given. For instance, a ring R is coherent iff any ultraproduct of f-injective modules is absolutely pure. We prove that the class S* \Sigma^* of f*-injective modules is closed under ultraproducts. On the other hand, S* \Sigma^* is not axiomatisable. For coherent rings R, S* \Sigma^* is axiomatisable iff every c0 \chi_0 -injective module is f*-injective. Further, it is shown that the class S \Sigma of f-injective modules is axiomatisable iff R is coherent and every c0 \chi_0 -injective module is f-injective. Finally, an f-injective module H, such that every module embeds in an ultraprower of H, is given. 相似文献
10.
In this paper, we introduce and study torsion-theoretic generalizations of singular and nonsingular modules by using the concept of τ-essential submodule for a hereditary torsion theory τ. We introduce two new module classes called τ-singular and non-τ-singular modules. We investigate some properties of these module classes and present some examples to show that these new module classes are different from singular and nonsingular modules. We give a characterization of τ-semisimple rings via non-τ-singular modules. We prove that if M∕τ(M) is non-τ-singular for a module M, then every submodule of M has a unique τ-closure. We give some properties of the torsion theory generated by the class of all τ-singular modules. We obtain a decomposition theorem for a strongly τ-extending module by using non-τ-singular modules. 相似文献
11.
We prove that for cardinalsτ satisfying τω=τ and forτ=ω
1, there do not exist universal Eberlein Compacts of weightτ, or universal WCG spaces of density characterτ. Ifτ is a strong limit cardinal of countable cofinality such universal spaces do exist. Thus under GCH universal spaces exist
forτ iff cof(τ)=ω.
The research of the second author was supported by a grant from the United States-Israel Binational Science Foundation and
the Fund for the Promotion of Research at the Technion. 相似文献
12.
A. I. Vinogradov 《Journal of Mathematical Sciences》1997,83(6):731-744
We obtain a spectral decomposition for number-theoretic convolutions of the form τ(n)×τ(n±l,χq), where the function τ is the number of divisors,χq is the quadratic Dirichlet character of module q, l is a fixed shift, and n is the summation parameter. This is done by using
the shortened functional equation for the convolution, obtained by the author (Zap. Nauchn. Semin. POMI,211, 104–119 (1994)). A presentation using the vector-matrix language is conducted for two convolutions with shifts ±l simultaneously,
which simplifies symbolic writing of the spectral decompositions.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 212, 1994, pp. 71–90.
Translated by B. M. Bekker. 相似文献
13.
Najmeh Dehghani Fatma A. Ebrahim S. Tariq Rizvi 《Journal of Pure and Applied Algebra》2019,223(1):422-438
The well known Schröder–Bernstein Theorem states that any two sets with one to one maps into each other are isomorphic. The question of whether any two (subisomorphic or) direct summand subisomorphic algebraic structures are isomorphic, has long been of interest. Kaplansky asked whether direct summands subisomorphic abelian groups are always isomorphic? The question generated a great deal of interest. The study of this question for the general class of modules has been somewhat limited. We extend the study of this question for modules in this paper. We say that a module Msatisfies the Schröder–Bernstein property (S-B property) if any two direct summands of M which are subisomorphic to direct summands of each other, are isomorphic. We show that a large number of classes of modules satisfy the S-B property. These include the classes of quasi-continuous, directly finite, quasi-discrete and modules with ACC on direct summands. It is also shown that over a Noetherian ring R, every extending module satisfies the S-B property. Among applications, it is proved that the class of rings R for which every R-module satisfies the S-B property is precisely that of pure-semisimple rings. We show that over a commutative domain R, any two quasi-continuous subisomorphic R-modules are isomorphic if and only if R is a PID. We study other conditions related to the S-B property and obtain characterizations of certain classes of rings via those conditions. Examples which delimit and illustrate our results are provided. 相似文献
14.
Jonas T. Hartwig 《Journal of Pure and Applied Algebra》2011,215(10):2352-2377
We define a notion of pseudo-unitarizability for weight modules over a generalized Weyl algebra (of rank one, with commutative coefficient ring R), which is assumed to carry an involution of the form X∗=Y, R∗⊆R. We prove that a weight module V is pseudo-unitarizable iff it is isomorphic to its finitistic dual V?. Using the classification of weight modules by Drozd, Guzner and Ovsienko, we obtain necessary and sufficient conditions for an indecomposable weight module to be isomorphic to its finitistic dual, and thus to be pseudo-unitarizable. Some examples are given, including Uq(sl2) for q a root of unity. 相似文献
15.
We study the concepts of the 𝒫C-projective and the ?C-injective dimensions of a module in the noncommutative case, weakening the condition of C being semidualizing. We give the relations between these dimensions and the C-relative Gorenstein dimensions (GC-projective and GC-injective dimensions) of the module. Finally, we compare, in some circumstances, the global 𝒫C-projective dimension of a ring and the global dimension of the endomorphisms ring of C. 相似文献
16.
《Quaestiones Mathematicae》2013,36(4):401-409
Abstract A module is said to be copure injective if it is injective with respect to all modules A ? B with B/A injective. We first characterize submodules that have the extension property with respect to copure injective modules. Then we characterize commutative rings with finite self injective dimension in terms of copure injective modules. Finally, we show that the quotient categories of reduced copure injective modules and reduced h- divisible modules are isomorphic. 相似文献
17.
In this article, we introduce the concept of IFP-flat (resp., IFP-injective) modules as nontrivial generalization of flat (resp., injective) modules. We investigate the properties of these modules in various ways. For example, we show that the class of IFP-flat (resp., IFP-injective) modules is closed under direct products and direct sums. Therefore, the direct product of flat modules is not flat in general; however, the direct product of flat modules is IFP-flat over any ring. We prove that (⊥??, ??) is a complete cotorsion theory and (??, ??⊥) is a perfect cotorsion theory, where ?? stands for the class of all IFP-injective left R-modules, and ?? denotes the class of all IFP-flat right R-modules. 相似文献
18.
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
19.
We consider a finite dimensional k-algebraA and associate to each tilting module a cone in the Grothendieck groupK
0 of finitely generated A-modules. We prove that the set of cones associated to tilting modules of projective dimension at
most one defines a, not necessarily finite, fan Σ(A). IfA is of finite global dimension, the fan Σ(A) is smooth. Moreover, using the cone of a tilting module, we can associate a volume
to each tilting module. Using the fan and the volume, we obtain new proofs for several classical results; we obtain certain
convergent sums naturally associated to the algebraA and obtain criteria for the completeness of a list of tilting modules. Finally, we consider several examples.
Dedicated to O. Riemenschneider on the occasion of his 65th birthday 相似文献
20.
A. Haghany 《Periodica Mathematica Hungarica》1996,32(3):193-197
We generalize the well-known fact that for a pair of Morita equivalent ringsR andS their maximal rings of quotients are again Morita equivalent: If
n
(M) denotes the torsion theory cogenerated by the direct sum of the firstn+1 injective modules forming part of the minimal injective resolution ofM then
n
(R)=
n
(S) where is the category equivalenceR-ModS-Mod. Consequently the localized ringsR
n
(R) andS
n
(S) are Morita equivalent. 相似文献