共查询到20条相似文献,搜索用时 7 毫秒
1.
We define and investigate t-semisimple modules as a generalization of semisimple modules. A module M is called t-semisimple if every submodule N contains a direct summand K of M such that K is t-essential in N. T-semisimple modules are Morita invariant and they form a strict subclass of t-extending modules. Many equivalent conditions for a module M to be t-semisimple are found. Accordingly, M is t-semisiple, if and only if, M = Z 2(M) ⊕ S(M) (where Z 2(M) is the Goldie torsion submodule and S(M) is the sum of nonsingular simple submodules). A ring R is called right t-semisimple if R R is t-semisimple. Various characterizations of right t-semisimple rings are given. For some types of rings, conditions equivalent to being t-semisimple are found, and this property is investigated in terms of chain conditions. 相似文献
2.
A submodule N of a module M is idempotent if N = Hom(M, N)N. The module M is fully idempotent if every submodule of M is idempotent. We prove that over a commutative ring, cyclic idempotent submodules of any module are direct summands. Counterexamples are given to show that this result is not true in general. It is shown that over commutative Noetherian rings, the fully idempotent modules are precisely the semisimple modules. We also show that the commutative rings over which every module is fully idempotent are exactly the semisimple rings. Idempotent submodules of free modules are characterized. 相似文献
3.
Domain constants are numbers attached to regions in the complex plane ℂ. For a region Ω in ℂ, letd(Ω) denote a generic domain constant. If there is an absolute constantM such thatM
−1≤d(Ω)/d(Δ)≤M whenever Ω and Δ are conformally equivalent, then the domain constant is called quasiinvariant under conformal mappings.
IfM=1, the domain constant is conformally invariant. There are several standard problems to consider for domain constants. One
is to obtain relationships among different domain constants. Another is to determine whether a given domain constant is conformally
invariant or quasi-invariant. In the latter case one would like to determine the best bound for quasi-invariance. We also
consider a third type of result. For certain domain constants we show there is an absolute constantN such that |d(Ω)−d(Δ)|≤N whenever Ω and Δ and conformally equivalent, sometimes determing the best possible constantN. This distortion inequality is often stronger than quasi-invariance. We establish results of this type for six domain constants.
Research partially supported by a National Science Foundation Grant. 相似文献
4.
Let R be any ring. A right R-module M is called n-copure projective if Ext1(M, N) = 0 for any right R-module N with fd(N) ≤ n, and M is said to be strongly copure projective if Ext i (M, F) = 0 for all flat right R-modules F and all i ≥ 1. In this article, firstly, we present some general properties of n-copure projective modules and strongly copure projective modules. Then we define and investigate copure projective dimensions of modules and rings. Finally, more properties and applications of n-copure projective modules, strongly copure projective modules and copure projective dimensions are given over coherent rings with finite self-FP-injective dimension. 相似文献
5.
An R-module M is called principally quasi-injective if each R-hornomorphism from a principal submodule of M to M can be extended to an endomorphism of M. Many properties of principally injective rings and quasi-injective modules are extended to these modules. As one application, we show that, for a finite-dimensional quasi-injective module M in which every maximal uniform submodule is fully invariant, there is a bijection between the set of indecomposable summands of M and the maximal left ideals of the endomorphism ring of M Throughout this paper all rings R are associative with unity, and all modules are unital. We denote the Jacobson radical, the socle and the singular submodule of a module M by J(M), soc(M) and Z(M), respectively, and we write J(M) = J. The notation N ?ess M means that N is an essential submodule of M. 相似文献
6.
M. Domokos 《manuscripta mathematica》2002,108(1):123-133
Let M be a finite dimensional module over a finite dimensional basic K-algebra Λ, where K is an algebraically closed field. We associate with M a weight θ
M
(i.e. an element of the dual of the Grothendieck group of mod-Λ) in module theoretic terms. Let β be a dimension vector with
θ
M
(β)=0. We generalize a construction of relative invariants of quivers due to Schofield [S] and define a relative invariant
polynomial function d
M
β
on the variety of modules of dimension vector β, such that d
M
β
(N) = 0 for some module N if and only if there is a nonzero morphism from M to N. Assuming char (K) = 0, we conclude from the main result of Schofield-Van den Bergh [SV] that relative invariants of this form span all the
spaces of relative invariants. To get algebra generators of the algebra of semi-invariants it is sufficient to take the d
M
β
with M indecomposable.
Received: 31 July 2001 相似文献
7.
We study Hilbert functions of maximal CM modules over CM local rings. When A is a hypersurface ring with dimension d>0, we show that the Hilbert function of M with respect to is non-decreasing. If A=Q/(f) for some regular local ring Q, we determine a lower bound for e0(M) and e1(M) and analyze the case when equality holds. When A is Gorenstein a relation between the second Hilbert coefficient of M, A and SA(M)= (SyzA1(M*))* is found when G(M) is CM and depthG(A)≥d−1. We give bounds for the first Hilbert coefficients of the canonical module of a CM local ring and analyze when equality
holds. We also give good bounds on Hilbert coefficients of M when M is maximal CM and G(M) is CM. 相似文献
8.
Recently, Blecher and Kashyap have generalized the notion of W
*-modules over von Neumann algebras to the setting where the operator algebras are σ closed algebras of operators on a Hilbert space. They call these modules weak* rigged modules. We characterize the weak* rigged modules over nest algebras. We prove that Y is a right weak* rigged module over a nest algebra Alg(M){\rm{Alg}(\mathcal M)} if and only if there exists a completely isometric normal representation F{\Phi } of Y and a nest algebra Alg(N){\rm{Alg}(\mathcal N)} such that Alg(N) F(Y)Alg(M) ì F(Y){\rm{Alg}(\mathcal N) \Phi (Y)\rm{Alg}(\mathcal M)\subset \Phi (Y)} while F(Y){\Phi (Y)} is implemented by a continuous nest homomorphism from M{\mathcal M} onto N{\mathcal N} . We describe some properties which are preserved by continuous CSL homomorphisms. 相似文献
9.
Let k(x) be the field of fractions of the polynomial algebra k[x] over the field k. We prove that, for an arbitrary finite dimensional k-algebra Λ, any finitely generated Λ ⊗k k(x)-module M such that its minimal projective presentation admits no non-trivial selfextension is of the form M ≅ Nk(x), for some finitely generated Λ-module N. Some consequences are derived for tilting modules over the rational algebra Λ ⊗k k(x) and for some generic modules for Λ.
Received: 24 November 2003; revised: 11 February 2005 相似文献
10.
W. K. Nicholson 《代数通讯》2013,41(1):219-233
If M and N are modules, the concept of semiregularity (and regularity) of hom(M,N) is defined and studied, and the connection with the relative direct injective- and direct projective-properties is established. The relationship of semiregularity to the Jacobson radical of hom(M,N), to the singular and cosingular ideals of hom(M,N), and to the notion of lying over or under a direct summand, is described, and the basic results in the module case are extended. Communicated by R. Wisbauer. 相似文献
11.
For a ring R and a right R-module M, a submodule N of M is said to be δ-small in M if, whenever N+X=M with M/X singular, we have X=M. Let ℘ be the class of all singular simple modules. Then δ(M)=Σ{ L≤ M| L is a δ-small submodule of M} = Re
jm(℘)=∩{ N⊂ M: M/N∈℘. We call M δ-coatomic module whenever N≤ M and M/N=δ(M/N) then M/N=0. And R is called right (left) δ-coatomic ring if the right (left) R-module R
R(RR) is δ-coatomic. In this note, we study δ-coatomic modules and ring. We prove M=⊕
i=1
n
Mi is δ-coatomic if and only if each M
i (i=1,…, n) is δ-coatomic. 相似文献
12.
Let R be an arbitrary ring with identity and M a right R-module with S = EndR(M). Let F be a fully invariant submodule of M and I?1(F) denotes the set {m∈M:Im?F} for any subset I of S. The module M is called F-Baer if I?1(F) is a direct summand of M for every left ideal I of S. This work is devoted to the investigation of properties of F-Baer modules. We use F-Baer modules to decompose a module into two parts consists of a Baer module and a module determined by fully invariant submodule F, namely, for a module M, we show that M is F-Baer if and only if M = F⊕N where N is a Baer module. By using F-Baer modules, we obtain some new results for Baer rings. 相似文献
13.
Using the concept of prime submodule for M ∈ R-Mod, P ∈ Spec(M), and N ∈ σ[M], we define when N is P-Mtame \ (Mtame) module. This concept generalizes the concept\ of P-tame (tame) modules. For M ∈ R-Mod and τ ∈M-tors, we use the concept of τ M -Gabriel dimension and we study the relationship between Mtame modules and τ M -Gabriel dimension. We find equivalent conditions for a module M progenerator in σ[M] with τ M -Gabriel dimension to have τ M -Gabriel correspondence in terms of the P-Mtame modules. This result extends the results by Albu et al. and Kim and Krause. 相似文献
14.
We develop a theory of harmonic maps f:MN between singular spaces M and N. The target will be a complete metric space (N,d) of nonpositive curvature in the sense of A. D. Alexandrov. The domain will be a measurable space (M,) with a given Markov kernel p(x,dy) on it. Given a measurable map f:MN, we define a new map Pf:MN in the following way: for each xM, the point Pf(x)N is the barycenter of the probability measure p(x,f
–1(dy)) on N. The map f is called harmonic on DM if Pf=f on D. Our theory is a nonlinear generalization of the theory of Markov kernels and Markov chains on M. It allows to construct harmonic maps by an explicit nonlinear Markov chain algorithm (which under suitable conditions converges exponentially fast). Many smoothing and contraction properties of the linear Markov operator P
M,R
carry over to the nonlinear Markov operator P=P
M,N
. For instance, if the underlying Markov kernel has the strong Lipschitz Feller property then all harmonic maps will be Lipschitz continuous. 相似文献
15.
Let N be a right near-ring. Denote by C(N) the multiplicative center of N, and by N d the set of left-distributive elements of N. In general, C(N) need not be closed under the addition of N. However, the generalized center of N, GC(N) = {a ? N|an d = n d a for all n d ? N d }, is always a subnear-ring of N containing C(N). In this article, we study the problem of determining when C(N) is a subnear-ring of N. We show that, for certain classes of near-rings, C(N) is a subnear-ring of N if and only if C(N) = GC(N). Examples are given to show the limits of the theory. 相似文献
16.
Let d be a fixed positive integer. A Lucas d-pseudoprime is a Lucas pseudoprime N for which there exists a Lucas sequence U(P, Q) such that the rank of N in U(P, Q) is exactly (N − ε(N))/d, where ε is the signature of U(P, Q). We prove here that all but a finite number of Lucas d-pseudoprimes are square free. We also prove that all but a finite number of Lucas d-pseudoprimes are Carmichael-Lucas numbers. 相似文献
17.
Let R be a ring. M is said to be a minannihilator left R-module if r M l R (I) = IM for any simple right ideal I of R. A right R-module N is called simple-flat if Nl R (I) = l N (I) for any simple right ideal I of R. R is said to be a left simple-Baer (resp., left simple-coherent) ring if the left annihilator of every simple right ideal is a direct summand of R R (resp., finitely generated). We first obtain some properties of minannihilator and simple-flat modules. Then we characterize simple-coherent rings, simple-Baer rings, and universally mininjective rings using minannihilator and simple-flat modules. 相似文献
18.
A. Laradji 《Archiv der Mathematik》2005,84(5):385-391
Let N be a normal subgroup of a p-solvable group G and let M be a simple FN-module, where F is an algebraically closed field of characteristic p. Next, denote by IRR0(FG|M) the set of all simple FG-modules V lying over M such that the p-part of dimF V is as small as possible. In this paper, |IRR0(FG|M)| and the vertices of modules in IRR0(FG|M) are determined. The p-blocks of G to which modules in IRR0(FG|M) belong are also determined.Received: 5 December 2003 相似文献
19.
Let A be a tame concealed or tubular algebra and d the dimension-vector of a periodic module with respect to the action of the Auslander–Reiten translation. We prove that the affine variety mod
A
(d) of all A-modules of dimension-vector d is a normal complete intersection. Moreover, we show that a module M in mod
A
(d) is nonsingular if and only if Ext
A
2(M,M)=0. 相似文献
20.
Sohrab Sohrabi Laleh Mir Yousef Sadeghi Mahdi Hanifi Mostaghim 《Czechoslovak Mathematical Journal》2012,62(1):105-110
Let R be a commutative Noetherian ring, a an ideal of R, M an R-module and t a non-negative integer. In this paper we show that the class of minimax modules includes the class of AF modules. The main result is that if the R-module Ext
R
t
(R/a,M) is finite (finitely generated), H
a
i
(M) is a-cofinite for all i < t and H
a
t
(M) is minimax then H
a
t
(M) is a-cofinite. As a consequence we show that if M and N are finite R-modules and H
a
i
(N) is minimax for all i < t then the set of associated prime ideals of the generalized local cohomology module H
a
t
(M,N) is finite. 相似文献