共查询到20条相似文献,搜索用时 43 毫秒
1.
广义幂级数环上的PS模 总被引:1,自引:0,他引:1
Let R be a commutative ring and(S,≤)a strictly totally ordered monoid which satisfies the condition that 0≤s for every s ∈ S,In this paper we show that if RM is a PS-module,then the module [[M^s,≤]]of generalized power series over M is a PS [[R^s,≤]]-module. 相似文献
2.
Let R be a ring with unit element, and A a left R-module. A is called FP-injective if ExtR′(P, A)=0 for every finitely presented R-module P. Let ER(A) denote the injective hull of A. In the paper we prove by means of inverse limit functor that any module A Over coherent ring R has the minimum FP-injective submodule eR(A) in ER(A) which contains A and can be defined as the FP-injective hull of A. 相似文献
3.
关于拟AP内射模的注记 总被引:2,自引:0,他引:2
Let R be a ring.A right R-module M with S=End(MR)is called aquasi AP-injective module,if,for any s ∈ S,there exists a left ideal X_s of S such thatl_s(ker s)=SsX_s.Let M be a quasi AP-injective module which is a self-generator.We show that for such a module,if S is semiprime,then every maximal kernel of S isa direct summand of M.Furthermore,if ker(a_1)ker(a_2a_1)ker(a_3a_2a_1)satisfy the ascending conditions for any sequence a_1,a_2,a_3,...∈ S,then S is rightperfect.In this paper,we give a series of results which extend and generalize resultson AP-injective rings. 相似文献
4.
Let A be a commutative ring with unit element, and let M be a Λ-module and σ∈HomΛ (M, M). Then a non-empty subset N of M is called a σ-submodule of the Λ-module M, if (1) a-b∈N for all a, bg∈N, and (2) λσ(α)∈N and x-σ(x)∈N for all λ∈Λ, α∈N, x∈M. Let N be a σ-submodule of M. N is said to be a primary σ-submodule of the Λ-module M, if (1) N≠M, and (2) whenever λ∈Λ, x∈M and λσ(x) ∈N, then either x∈N or λkσ(M)?N for some positive integer h. This paper is intended to show (1) that if M satisfies maximal condition of σ-submodule, and K is a σ-submodule of M, then K is a finite intersection of primary σ-submodules, and (2) that the uniqueness on the normal expression of σ-submodule of the Λ-module. Also, some results of fractional module have been obtained. 相似文献
5.
ZhiXiangWU 《数学学报(英文版)》2005,21(2):249-260
In this paper, we prove that R is a two-sided Artinian ring and J is a right annihilator ideal if and only if (i) for any nonzero right module, there is a nonzero linear map from it to a projective module; (ii) every submodule of RR is not a radical module for some right coherent rings. We call a ring a right X ring if Homa(M, R) = 0 for any right module M implies that M = 0. We can prove some left Goldie and right X rings are right Artinian rings. Moreover we characterize semisimple rings by using X rings. A famous Faith‘s conjecture is whether a semipimary PF ring is a QF ring. Similarly we study the relationship between X rings and QF and get many interesting results. 相似文献
6.
Jia Feng Lü 《数学学报(英文版)》2009,25(6):1015-1030
The so-called weakly d-Koszul-type module is introduced and it turns out that each weakly d-Koszul-type module contains a d-Koszul-type submodule. It is proved that, M ∈ W H J^d(A) if and only if M admits a filtration of submodules: 0 belong to U0 belong to U1 belong to ... belong to Up = M such that all Ui/Ui-1 are d-Koszul-type modules, from which we obtain that the finitistic dimension conjecture holds in W H J^d(A) in a special case. Let M ∈ W H J^d(A). It is proved that the Koszul dual E(M) is Noetherian, Hopfian, of finite dimension in special cases, and E(M) ∈ gr0(E(A)). In particular, we show that M ∈ W H J^d(A) if and only if E(G(M)) ∈ gr0(E(A)), where G is the associated graded functor. 相似文献
7.
In this paper,we introduce the signed weak gliding hump property in a dual pair with the sturcture of a system of sections and show that if a dual pair [E,F] has the signed weak gliding hump property,then the β-dual space of E is a weak sequentially complete space if and only if for every n ∈N,(F^[n],σ(F^[n],E^[n]))is sequentially complete,Furthermore,we also prove that if [E,F] has the signed weak gliding hump property,then (E,τ(E,F^(β))is an AK-space. 相似文献
8.
In this paper we have proved the theorem: Let p>1, and E be a real normed linear space, if the Lp-orthogonality in E satisfies one of the following conditions 1) homogeneity 2) additivity 3) x⊥Lpy implies x⊥Jy 4) x⊥Jy implies x⊥Lpy, then E is an abstract Euclidean space and there must be p=2. We also proved anR. C. James' result-If for every element x of a normed linear space E therecan be found a nonzero element orthogonal to x by Roberts' definition in each two dimensional linear subset containing x, then E is an abstract Euclidean space——which had not been proved. Finally, we point out that if one of the James′,Lp-,isosceles, Pythagorean and (α,β)-orthogonalities defined in E implies Roberts′ orthogonality then E is an abstract Euclidean space. 相似文献
9.
in this psper,we investigate nore general rings than GPP-rings,called fPP-rings.First,we in-vestigate fPP-rings and their classical quotient quotient rings.We ptove (1) fPP-rings are f-quasi-regular rings.(2)R is a fPP-ring then Q(R) is fPP-ring.(3)R= iRi is a fPP-ring if and only if every Ri is a fPP-ring.Second,we present a characterization of fPP-ring via fP-injectivity,we prove that R is a fPP-ring if and only if every quotient module of a imjective R-module is fP-injectiv if and only ifevery quotient module of a P-injective R-module is fP-injective.Third,we study how fPP-rings are related to von Neu-mann regular rings,we prove that R is von Nevmann regular if and only if R is fPP-ring and for every α∈R,there is b∈E(R) and d∈R suth that α=f(α)b and f(α)=f^2(α) d for some f∈F(R).Finally,we give a example of fPP-ring which is not GPP-ring. 相似文献
10.
On Maximal Injectivity 总被引:5,自引:0,他引:5
Ming Yi WANG Guo ZHAO 《数学学报(英文版)》2005,21(6):1451-1458
A right R-module E over a ring R is said to be maximally injective in case for any maximal right ideal m of R, every R-homomorphism f : m → E can be extended to an R-homomorphism f^1 : R → E. In this paper, we first construct an example to show that maximal injectivity is a proper generalization of injectivity. Then we prove that any right R-module over a left perfect ring R is maximally injective if and only if it is injective. We also give a partial affirmative answer to Faith's conjecture by further investigating the property of maximally injective rings. Finally, we get an approximation to Faith's conjecture, which asserts that every injective right R-module over any left perfect right self-injective ring R is the injective hull of a projective submodule. 相似文献
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12.
Pham Thi Thu Thuy 《Journal of Mathematical Sciences》2014,197(5):658-678
A subgroup A of an Abelian group G is called its absolute ideal if A is an ideal of any ring on G. An Abelian group is called an RAI-group if there exists a ring on it in which every ideal is absolute. The problem of describing RAI-groups was formulated by L. Fuchs (Problem 93). In this paper, absolute ideals of torsion Abelian groups and torsion Abelian RAI-groups are described. 相似文献
13.
We prove that the group T(G) of endo-trivial modules for a noncyclic finite p-group G is detected on restriction to the family of subgroups which are either elementary Abelian of rank 2 or (almost) extraspecial. This result is closely related to the problem of finding the torsion subgroup of T(G). We give the complete structure of T(G) when G is dihedral, semi-dihedral, or quaternion. 相似文献
14.
Pham Thi Thu Thuy 《Journal of Mathematical Sciences》2014,197(5):679-683
This paper is devoted to the study of Abelian afi-groups. A subgroup A of an Abelian group G is called its absolute ideal if A is an ideal of any ring on G. We will call an Abelian group an afi-group if all of its absolute ideals are fully invariant subgroups. In this paper, we will describe afi-groups in the class of fully transitive torsion groups (in particular, separable torsion groups) and divisible torsion groups. 相似文献
15.
John Dauns 《Annali di Matematica Pura ed Applicata》1989,154(1):49-81
Sunto Si studia un funtore contravariante dalla categoria di tutti gli anelli associativi con identità (con opportuni omomorfismi) nella categoria dei reticoli Booleani completi (equivalentemente, degli anelli Booleani completi). Per ogni anello R il reticolo (R) è l'insieme delle classi di equivalenza [A] modulo un'opportuna equivalenza, ove A varia nella classe degli R-moduli destri non singolari.
The author is grateful to his colleagueLaszlo Fuchs for his advice and encouragement. The author thanks the referee for a careful reading of the paper, and his useful comments. 相似文献
The author is grateful to his colleagueLaszlo Fuchs for his advice and encouragement. The author thanks the referee for a careful reading of the paper, and his useful comments. 相似文献
16.
Bhargav Bhatt 《Journal of Pure and Applied Algebra》2019,223(5):1940-1945
Given a commutative ring A and a finitely generated ideal I, we prove that -torsion A-modules that are also I-adically complete (or merely derived I-complete) must have bounded -torsion, i.e., they are killed by for some . 相似文献
17.
A conjecture due to Zassenhaus asserts that if G is a finite group then any torsion unit in ?G is conjugate in ?G to an element of G. Here, a weaker form of this conjecture is proved for some infinite groups. 相似文献
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19.
Radoslav M. Dimitrić 《Acta Appl Math》2008,100(2):105-112
This paper generalizes a number of results obtained by Dimitrić in (Glas. Mat. 21(41):327–329, 1986; Proceedings of Hobart Conference on Rings, Modules and Radicals 1987, 204:41–50, Gordon and Breach, 1989) and Dimitrić and Goldsmith in (Glas. Mat. 23(43):241–246, 1988). The original papers were restricted to the category of Abelian groups and orthogonality was to the group of integers ℤ.
Here, we are in a general Abelian category with products and coproducts, with applications to module categories and further
to modules over PID’s. Another generalization is in replacing ℤ by an entire class of subobjects
of the underlying category. We examine properties of the torsion class
, Hom(T,C)=0} in relation to purity, direct summands and indecomposability as well as commutation with direct products, for example.
Of special interest are members of this class when
is a class of slender objects in the ground category; in this case, members of
are called ortho-slender objects. In a sense, ortho-slenderness represents complementary, if not dual, notion to slenderness.
相似文献
20.