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1.
Ihsen Yengui 《Journal of Pure and Applied Algebra》2003,178(2):215-224
We propose to give positive answers to the open questions: is R(X,Y) strong S when R(X) is strong S? is R stably strong S (resp., universally catenary) when R[X] is strong S (resp., catenary)? in case R is obtained by a (T,I,D) construction. The importance of these results is due to the fact that this type of ring is the principal source of counterexamples. Moreover, we give an answer to the open questions: is R〈X1,…,Xn〉 residually Jaffard (resp., totally Jaffard) when R(X1,…,Xn) is ? We construct a three-dimensional local ring R such that R(X1,…,Xn) is totally Jaffard (and hence, residually Jaffard) whereas R〈X1,…,Xn〉 is not residually Jaffard (and hence, not totally Jaffard). 相似文献
2.
It is proved that if a K?the space λ1(A) is distinguished and E is an arbitrary Fréchet space then every reflexive map T: λ1(A)→E (i.e., T maps bounded sets into relatively weakly compact ones) factorizes through a reflexive Fréchet space. An analogous result
is proved for Montel maps (i.e., which map bounded sets into relatively compact ones). The result is a consequence of the
fact proved also in this paper that, for a distinguished λ1(A) space, the spaces of reflexive maps R(λ1(A), C(K)) and of Montel maps M(λ1(A), C(K)) are the Mackey completions of the spaces of weakly compact and compact maps, respectively. Consequences for spaces of vector-valued
(weakly) continuous functions are also obtained.
Received: 24 November 1997 / Revised version: 14 May 1998 相似文献
3.
《代数通讯》2013,41(5):1853-1869
In this paper, we determine necessary and sufficient conditions for the group ring D[G] to be a BFD (resp., an FFD, an SFFD). Also we give necessary and sufficient conditions for the monoid domain D[S] to be a BFD (resp., an FFD, an SFFD). In addition, we characterize when themonoid domain D[S] is a UFD in terms of 2-factoriality. 相似文献
4.
We call a commutative ring R an F IN -ring (resp., F SA-ring) if for any two finitely generated I, J ?R we have Ann(I)+Ann(J )=Ann(I∩J ) (resp., there is K ? R such that Ann(I)+Ann(J )=Ann(K)). Moreover, we extend this concepts to αIN -rings and αSA-rings where α is a cardinal number. The class of F SA-rings includes the class of all SA-rings (hence all IN -rings) and all P P -rings (hence all Baer-rings). In this paper, after giving some properties of αSA-rings, we prove that a reduced ring R is αSA if and only if it is an αIN -ring. Consequently, C(X) is an F SA-ring if and only if C(X) is an F IN -ring and equivalently X is an F -space. Moreover, for a commutative ring R, we have shown that R is a Baer-ring if and only if R is a reduced IN -ring. A topological space X is said to be an αU E-space if the closure of any union with cardinal number less than α of clopen subsets is open. Topological properties of αU E-spaces are investigated. Finally, we show that a completely regular Hausdor? space X is an αU E-space if and only if C(X) is an αEGE-ring. 相似文献
5.
《Quaestiones Mathematicae》2013,36(3-4):303-309
Abstract For a completely regular space X and a normed space E let Ck (x, E) (resp., Cp (x, E)) be the set of all E-valued continuous maps on X endowed with the compact-open (resp., pointwise convergence) topology. It is shown that the set of all F-valued linear continuous maps on Ck (x, E) when equipped with the topology of uniform convergence on the members of some families of bounded subsets of Ck (x, E) is a complete uniform space if F is a Band space and X is Dieudonné complete. This result is applied to prove that Dieudonné completeness is preserved by linear quotient surjections from Ck (x, E) onto Ck (Y, E) (resp., from Cp (x, E) onto Cp (x, E)) provided E, F are Band spaces and Y is a k-space. 相似文献
6.
Convergence of the efficient sets 总被引:2,自引:0,他引:2
LetA
n,n=1, 2, ... be nonempty subsets of a linear metric spaceE andC
n, n=1, 2, ... convex cones ofE. We consider the efficient sets Min(A
n, Cn) and the aim of this paper is to show that under suitable conditions, the convergence ofA
n andC
n toA andC respectively, implies the convergence of Min(A
n,C
n) to Min(A, C). Several illustrative examples are given which clarify the results. 相似文献
7.
Marek Golasiński 《Topology and its Applications》2011,158(14):1756-1761
The author surveys, summarizes and generalizes results of Golasiński and Henriksen, and of others, concerning certain residue class rings.Let A(R) denote the ring of analytic functions over reals R and E(K) the ring of entire functions over R or complex numbers C. It is shown that if m is a maximal ideal of A(R), then A(R)/m is isomorphic either to the reals or a real-closed field that is η1-set, while if m is a maximal ideal of E(K), then E(K)/m is isomorphic to one of these latter two fields or to complex numbers. 相似文献
8.
A ring R with 1 is called an E-ring if EndZR is ring-isomorphic to R under the canonical homomorphism taking the value 1σ for any σ∈EndZR. Moreover R is an absolute E-ring if it remains an E-ring in every generic extension of the universe. E-rings are an important tool for algebraic topology as explained in the introduction. The existence of an E-ring R of each cardinality of the form λℵ0 was shown by Dugas, Mader and Vinsonhaler (1987) [9]. We want to show the existence of absolute E-rings. It turns out that there is a precise cardinal-barrier κ(ω) for this problem: (The cardinal κ(ω) is the first ω-Erd?s cardinal defined in the introduction. It is a relative of measurable cardinals.) We will construct absolute E-rings of any size λ<κ(ω). But there are no absolute E-rings of cardinality ?κ(ω). The non-existence of huge, absolute E-rings ?κ(ω) follows from a recent paper by Herden and Shelah (2009) [24] and the construction of absolute E-rings R is based on an old result by Shelah (1982) [31] where families of absolute, rigid colored trees (with no automorphism between any distinct members) are constructed. We plant these trees into our potential E-rings with the aim to prevent unwanted endomorphisms of their additive group to survive. Endomorphisms will recognize the trees which will have branches infinitely often divisible by primes. Our main result provides the existence of absolute E-rings for all infinite cardinals λ<κ(ω), i.e. these E-rings remain E-rings in all generic extensions of the universe (e.g. using forcing arguments). Indeed all previously known E-rings (Dugas, Mader and Vinsonhaler, 1987 [9]; Göbel and Trlifaj, 2006 [23]) of cardinality ?ℵ02 have a free additive group R+ in some extended universe, thus are no longer E-rings, as explained in the introduction. Our construction also fills all cardinal-gaps of the earlier constructions (which have only sizes λℵ0). These E-rings are domains and as a by-product we obtain the existence of absolutely indecomposable abelian groups, compare Göbel and Shelah (2007) [22]. 相似文献
9.
Mohamed Jaouhar Ben Abdallah 《Journal of Pure and Applied Algebra》2008,212(10):2170-2175
If 1≤n<∞ and R⊆S are integral domains, then (R,S) is called an n-catenarian pair if for each intermediate ring T (that is each ring T such that R⊆T⊆S) the polynomial ring in n indeterminates, T[n] is catenarian. This implies that (R,S) is m-catenarian for all m<n. The main purpose of this paper is to prove that 1-catenarian and universally catenarian pairs are equivalent in several cases. An example of a 1-catenarian pair which is not 2-catenarian is given. 相似文献
10.
In this paper, we study Gorenstein injective modules over a local Noetherian ring R. For an R-module M, we show that M is Gorenstein injective if and only if Hom
R
(Ȓ,M) belongs to Auslander category B(Ȓ), M is cotorsion and Ext
i
R
(E,M) = 0 for all injective R-modules E and all i > 0.
Received: 24 August 2006 Revised: 30 October 2006 相似文献
11.
K. Varadarajan 《代数通讯》2013,41(2):771-783
The main results proved in this paper are: 1. For any non-zero vector space V Dover a division ring D, the ring R= End(V D) is hopfian as a ring 2. Let Rbe a reduced π-regular ring &; B(R) the boolean ring of idempotents of R. If B(R) is hopfian so is R.The converse is not true even when Ris strongly regular. 3. Let Xbe a completely regular spaceC(X) (resp. C ?(X)) the ring of real valued (resp. bounded real valued) continuous functions on X. Let Rbe any one of C(X) or C ?(X). Then Ris an exchange ring if &; only if Xis zero dimensional in the sense of Katetov. for any infinite compact totally disconnected space X C(X) is an exchange ring which is not von Neumann regular. 4. Let Rbe a reduced commutative exchange ring. If Ris hopfian so is the polynomial ring R[T 1,…,T n] in ncommuting indeterminates over Rwhere nis any integer ≥ 1. 5. Let Rbe a reduced exchange ring. If Ris hopfian so is the polynomial ring R[T]. 相似文献
12.
Stability in vector-valued and set-valued optimization 总被引:8,自引:0,他引:8
X. X. Huang 《Mathematical Methods of Operations Research》2000,52(2):185-193
In this paper, we discuss the stability of the sets of efficient points of vector-valued and set-valued optimization problems when the data (E n,f n) (resp. (E n, F n)) of the approximate problems converge to the data (E, f) (resp. (E, F)) of the original problem in the sense of Painleve-Kuratowski or Mosco. Our results improve and generalize those obtained by Attouch and Riahi in Section 5 in [1]. 相似文献
13.
In a series of papers Mauduit and Sárközy (partly with further coauthors) studied finite pseudorandom binary sequences. In particular, one of the most important applications of pseudorandomness is cryptography. If, e.g., we want to use a binary sequence EN{-1,+1}N (after transforming it into a bit sequence) as a key stream in the standard Vernam cipher [A. Menezes, P. van Oorschot, R. Vanstone, Handbook of Applied Cryptography, CRC Press, Boca Raton, 1997], then EN must possess certain pseudorandom properties. Does EN need to possess both small well-distribution measure and, for any fixed small k, small correlation measure of order k? In other words, if W(EN) is large, resp. Ck(EN) is large for some fixed small k, then can the enemy utilize this fact to break the code? The most natural line of attack is the exhaustive search: the attacker may try all the binary sequences EN{-1,+1}N with large W(EN), resp. large Ck(EN), as a potential key stream. Clearly, this attack is really threatening only if the number of sequences EN{-1,+1}N with
- (i) large W(EN), resp.
- (ii) large Ck(EN)
14.
Najib Mahdou 《代数通讯》2013,41(3):1066-1074
In this work, we give a sufficient condition to resolve Costa's first conjecture for each positive integer n and d with n ≥ 4. Precisely, we show that if there exists a local ring (A, M) such that λ A (M) = n, and if there exists an (n + 2)-presented A-submodule of M m , where m is a positive integer (for instance, if M contains a regular element), then we may construct an example of (n + 4, d)-ring which is neither an (n + 3, d)-ring nor an (n + 4, d ? 1)-ring. Finally, we construct a local ring (B, M) such that λ B (M) = 0 (resp., λ B (M) = 1) and so we exhibit for each positive integer d, an example of a (4, d)-ring (resp., (5, d)-ring) which is neither a (4, d ? 1)-ring (resp., neither a (5, d ? 1)-ring) nor a (2, d′)-ring (resp., nor a (3, d′)-ring) for each positive integer d′. 相似文献
15.
《Quaestiones Mathematicae》2013,36(3-4):219-234
Abstract For a unital module V over a commutative ring R, let C denote the collection of cyclic submodules. The ring ?R(V;C) = {f ε EndR V |f(C) ?C, ?C εR (V;C) has been the object of several recent studies in which the structure of ?R(V;C) is related to the triple (V, R,C). Here we introduce a new ring HR(V;C) containing ?(V;C) and investigate its structure in terms of the parameters (V, R, C). 相似文献
16.
On the Isolated Points of the Spectrum of Paranormal Operators 总被引:1,自引:0,他引:1
Atsushi Uchiyama 《Integral Equations and Operator Theory》2006,55(1):145-151
For paranormal operator T on a separable complex Hilbert space
we show that (1) Weyl’s theorem holds for T, i.e., σ(T) \ w(T) = π00(T) and (2) every Riesz idempotent E with respect to a non-zero isolated point λ of σ(T) is self-adjoint (i.e., it is an orthogonal projection) and satisfies that ranE = ker(T − λ) = ker(T − λ)*. 相似文献
17.
Alexandre B. Tchernev 《Advances in Mathematics》2007,208(1):75-134
Let k be a field, let R=k[x1,…,xm] be a polynomial ring with the standard Zm-grading (multigrading), let L be a Noetherian multigraded R-module, and let be a finite free multigraded presentation of L over R. Given a choice S of a multihomogeneous basis of E, we construct an explicit canonical finite free multigraded resolution T•(Φ,S) of the R-module L. In the case of monomial ideals our construction recovers the Taylor resolution. A main ingredient of our work is a new linear algebra construction of independent interest, which produces from a representation ? over k of a matroid M a canonical finite complex of finite dimensional k-vector spaces T•(?) that is a resolution of Ker?. We also show that the length of T•(?) and the dimensions of its components are combinatorial invariants of the matroid M, and are independent of the representation map ?. 相似文献
18.
Let D be an integral domain such that Int(D) ≠ K[X] where K is the quotient field of D. There is no known example of such a D so that Int(D) has finite elasticity. If E is a finite nonempty subset of D, then it is known that Int(E, D) = {f(X) ∈ K[X] | f(e) ∈ D for all e ∈ E} is not atomic. In this note, we restrict the notion of elasticity so that it is applicable to nonatomic domains. For each
real number r ≥ 1, we produce a ring of integer-valued polynomials with restricted elasticity r. We further show that if D is a unique factorization domain and E is finite with |E| > 1, then the restricted elasticity of Int(E, D) is infinite.
Part of this work was completed while the first author was on an Academic Leave granted by the Trinity University Faculty
Development Committee. 相似文献
19.
Let D be an integral domain and E a non-empty finite subset of D. For n ≧ 2, we show that D has the n-generator property if and only if Int(E, D) has the n-generator property if and only if Int(E, D) has the strong (n + 1)-generator property. Thus, iterating the Int(E, D) construction cannot produce Prüfer domains whose finitely generated ideals require an ever larger number of generators.
We also show that, for n ≧ 2, a non-zero polynomial f ∈Int(E, D) is a strong n-generator in Int(E, D) if and only if f (a) is a strong n-generator in D for all a ∈E.
Received: 15 July 2004 相似文献
20.
Let L be a finite-dimensional complex simple Lie algebra, L ? be the ?-span of a Chevalley basis of L, and L R = R ?? L ? be a Chevalley algebra of type L over a commutative ring R. Let 𝒩(R) be the nilpotent subalgebra of L R spanned by the root vectors associated with positive roots. A map ? of 𝒩(R) is called commuting if [?(x), x] = 0 for all x ∈ 𝒩(R). In this article, we prove that under some conditions for R, if Φ is not of type A 2, then a derivation (resp., an automorphism) of 𝒩(R) is commuting if and only if it is a central derivation (resp., automorphism), and if Φ is of type A 2, then a derivation (resp., an automorphism) of 𝒩(R) is commuting if and only if it is a sum (resp., a product) of a graded diagonal derivation (resp., automorphism) and a central derivation (resp., automorphism). 相似文献