共查询到20条相似文献,搜索用时 15 毫秒
1.
Gerald Beer 《Israel Journal of Mathematics》1987,58(2):205-212
IfA andB are closed nonempty sets in a locally convex space, the straight line path fromA toB is defined by the formulaφ(α)=cl (αA+(1−α)B), 0≦α≦1. IfA andB are convex, then continuity of the path with respect to the Hausdorff uniform topology is necessary for both connectedness
and path connectedness ofA toB within the convex sets so topologized. We also produce internal necessary and sufficient conditions for continuity of the
path between pairs of convex sets. 相似文献
2.
A set of operations on A is shown to be the set of linear term operations of some algebra on A if and only if it is closed under permutation of variables, addition of inessential variables, and composition, and if it
contains all projections. A Galois framework is introduced to describe the sets of operations that are closed under the operations
mentioned above, not necessarily containing all projections. The dual objects of this Galois connection are systems of pointed
multisets, and the Galois closed sets of dual objects are described accordingly. Moreover, the closure systems associated
with this Galois connection are shown to be uncountable (even if the closed sets of operations are assumed to contain all
projections). 相似文献
3.
The quaternion algebraB[j] over a commutative ringB with 1 defined byS. Parimala andR. Sridharan is generalized in two directions: (1) the ringB may be non-commutative with 1, and (2)j
2 may be any invertible element (not necessarily –1). LetG={} be an automorphism group ofB of order 2, andA={b inB| (b)=b}. LetB[j] be a generalized quaternion algebra such thataj (a) for eacha inB. It will be shown thatB is Galois (for non-commutative ring extensions) overA which is contained in the center ofB if and only ifB[j] is Azumaya overA. Also,A[j] is a splitting ring forB[j] such thatA[j] is Galois overA. Moreover, we shall determine which automorphism group ofA[j] is a Galois group. 相似文献
4.
A ring extension A ‖ B is depth two if its tensor-square satisfies a projectivity condition w.r.t. the bimodules A A B and B A A . In this case the structures (A ? B A) B and End B A B are bialgebroids over the centralizer C A (B) and there is a certain Galois theory associated to the extension and its endomorphism ring. We specialize the notion of depth two to induced representations of semisimple algebras and character theory of finite groups. We show that depth two subgroups over the complex numbers are normal subgroups. As a converse, we observe that normal Hopf subalgebras over a field are depth two extensions. A generalized Miyashita–Ulbrich action on the centralizer of a ring extension is introduced, and applied to a study of depth two and separable extensions, which yields new characterizations of separable and H-separable extensions. With a view to the problem of when separable extensions are Frobenius, we supply a trace ideal condition for when a ring extension is Frobenius. 相似文献
5.
George Szeto 《代数通讯》2013,41(12):3979-3985
Let B be a Galois algebra over a commutative ring R with Galois group G such that B H is a separable subalgebra of B for each subgroup H of G. Then it is shown that B satisfies the fundamental theorem if and only if B is one of the following three types: (1) B is an indecomposable commutative Galois algebra, (2) B = Re ⊕ R(1 ? e) where e and 1 ? e are minimal central idempotents in B, and (3) B is an indecomposable Galois algebra such that for each separable subalgebra A, V B (A) = ?∑ g∈G(A) J g , and the centers of A and B G(A) are the same where V B (A) is the commutator subring of A in B, J g = {b ∈ B | bx = g(x)b for each x ∈ B} for a g ∈ G, and G(A) = {g ∈ G | g(a) = a for all a ∈ A}. 相似文献
6.
In this paper, we prove some theorems on fuzzy sets. We first show that, in order to demonstrate that the equality of shadows ofA andB implies the equality ofA andB, it is necessary to assume thatA andB are closed and thatS
H
(A)=S
H
(B) for any closed hyperplane hyperplaneH. We also obtain a separation theorem for two convex fuzzy sets in a Hilbert space. Finally, we investigate results relating to minimax theorems for fuzzy sets. We obtain a necessary and sufficient condition for compactness.The authors wish to express their sincere thanks to Professor Hisaharu Umegaki for his invaluable suggestions and advice. 相似文献
7.
Let R be a domain, complete with respect to a norm which defines a non-discrete topology on R. We prove that the quotient field of R is ample, generalizing a theorem of Pop. We then consider the case where R is a ring of arithmetic power series which are holomorphic on the closed disc of radius 0<r<1 around the origin, and apply the above result to prove that the absolute Galois group of the quotient field of R is semi-free. This strengthens a theorem of Harbater, who solved the inverse Galois problem over these fields. 相似文献
8.
Let A and B be closed operators on Banach spaces X and Y. Assume that A and B have nonempty resolvent sets and that the spectra of A and B are unbounded. Let α be a uniform cross norm on X ? Y. Using the Gelfand theory and resolvent algebra techniques, a spectral mapping theorem is proven for a certain class of rational functions of A and B. The class of admissable rational functions (including polynomials) depends on the spectra of A and B. The theory is applied to the cases A ? I + I ? B and A ? B where A and B are the generators of bounded holomorphic semigroups. 相似文献
9.
A topological space is called resolvable if it is a union of two disjoint dense subsets, and is n-resolvable if it is a union of n mutually disjoint dense subsets. Clearly a resolvable space has no isolated points. If f is a selfmap on X, the sets A?X with f (A)?A are the closed sets of an Alexandroff topology called the primal topology 𝒫(f ) associated with f. We investigate resolvability for primal spaces (X, 𝒫(f)). Our main result is that an Alexandroff space is resolvable if and only if it has no isolated points. Moreover, n-resolvability and other related concepts are investigated for primal spaces. 相似文献
10.
We study comodule functors for comonads arising from mixed distributive laws. Their Galois property is reformulated in terms
of a (so-called) regular arrow in Street’s bicategory of comonads. Between categories possessing equalizers, we introduce
the notion of a regular adjunction. An equivalence is proven between the category of pre-torsors over two regular adjunctions
(N
A
,R
A
) and (N
B
,R
B
) on one hand, and the category of regular comonad arrows (R
A
,ξ) from some equalizer preserving comonad
\mathbb C{\mathbb C} to N
B
R
B
on the other. This generalizes a known relationship between pre-torsors over equal commutative rings and Galois objects of
coalgebras. Developing a bi-Galois theory of comonads, we show that a pre-torsor over regular adjunctions determines also
a second (equalizer preserving) comonad
\mathbb D{\mathbb D} and a co-regular comonad arrow from
\mathbb D{\mathbb D} to N
A
R
A
, such that the comodule categories of
\mathbb C{\mathbb C} and
\mathbb D{\mathbb D} are equivalent. 相似文献
11.
Otto Kerner Andrzej Skowroński Kunio Yamagata Dan Zacharia 《Central European Journal of Mathematics》2004,2(1):103-111
The strong global dimension of a finite dimensional algebra A is the maximum of the width of indecomposable bounded differential complexes of finite dimensional projective A-modules. We prove that the strong global dimension of a finite dimensional radical square zero algebra A over an algebraically closed field is finite if and only if A is piecewise hereditary. Moreover, we discuss results concerning the finiteness of the strong global dimension of algebras
and the related problem on the density of the push-down functors associated to the canonical Galois coverings of the trivial
extensions of algebras by their repetitive algebras. 相似文献
12.
Gregory L. McColm 《Mathematical Logic Quarterly》1992,38(1):293-298
It is known that for two given countable sets of unary relations A and B on ω there exists an infinite set H ? ω on which A and B are the same. This result can be used to generate counterexamples in expressibility theory. We examine the sharpness of this result. 相似文献
13.
Let F be an algebraically closed field and let A and B be arbitrary finite dimensional simple algebras over F. We prove that A and B are isomorphic if and only if they satisfy the same identities. 相似文献
14.
Yves Diers 《Journal of Geometry》1999,65(1-2):54-76
For an arbitrary algebraic theory T and a prescribed T-algebraL, the geometrical category AfAlgSet(L) of affine algebraic sets over the affine lineL is build up. It is proved to be dually equivalent to the category FcAlg(L) of functional T-algebras overL. The Galois theory ofL is defined and a Galois duality established. These geometrical categories are characterized up to an equivalence of categories. 相似文献
15.
An Abelian group A is called correct if for any Abelian group B isomorphisms A ≅ B′ and B ≅ A′, where A′ and B′ are subgroups of the groups A and B, respectively, imply the isomorphism A ≅ B. We say that a group A is determined by its subgroups (its proper subgroups) if for any group B the existence of a bijection between the sets of all subgroups (all proper subgroups) of groups A and B such that corresponding subgroups are isomorphic implies A ≅ B. In this paper, connections between the correctness of Abelian groups and their determinability by their subgroups (their
proper subgroups) are established. Certain criteria of determinability of direct sums of cyclic groups by their subgroups
and their proper subgroups, as well as a criterion of correctness of such groups, are obtained.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 3, pp. 21–36, 2003. 相似文献
16.
Let k be an algebraically closed field. Let P(X
11, . . . , X
nn
, T) be the characteristic polynomial of the generic matrix (X
ij
) over k. We determine its singular locus as well as the singular locus of its Galois splitting. If X is a smooth quasi-projective surface over k and A an Azumaya algebra on X of degree n, using a method suggested by M. Artin, we construct finite smooth splittings for A of degree n over X whose Galois closures are smooth. 相似文献
17.
Martin Rmoutil 《Czechoslovak Mathematical Journal》2013,63(1):205-217
In the present article we provide an example of two closed non-σ-lower porous sets A,B ? ? such that the product A × B is lower porous. On the other hand, we prove the following: Let X and Y be topologically complete metric spaces, let A ? X be a non-σ-lower porous Suslin set and let B ? Y be a non-σ-porous Suslin set. Then the product A × B is non-σ-lower porous. We also provide a brief summary of some basic properties of lower porosity, including a simple characterization of Suslin non-σ-lower porous sets in topologically complete metric spaces. 相似文献
18.
A well‐known conjecture of Erd?s states that given an infinite graph G and sets A, ? V(G), there exists a family of disjoint A ? B paths ?? together with an A ? B separator X consisting of a choice of one vertex from each path in ??. There is a natural extension of this conjecture in which A, B, and X may contain ends as well as vertices. We prove this extension by reducing it to the vertex version, which was recently proved by Aharoni and Berger. © 2005 Wiley Periodicals, Inc. J Graph Theory 50: 199–211, 2005 相似文献
19.
Let B be an Azumaya Galois extension or a DeMeyer-Kanzaki Galois extension with Galois group G. Equivalent conditions are given for a separable subextension of a Galois extension in the skew group ring B * G being an invariant subring of a subgroup of the Galois group G.AMS Subject Classification (2000): 16S35, 16W20. 相似文献
20.
Rafał Bocian Thorsten Holm Andrzej Skowroński 《Central European Journal of Mathematics》2004,2(1):67-75
Auslander’s representation dimension measures how far a finite dimensional algebra is away from being of finite representation
type. In [1], M. Auslander proved that a finite dimensional algebra A is of finite representation type if and only if the representation dimension of A is at most 2. Recently, R. Rouquier proved that there are finite dimensional algebras of an arbitrarily large finite representation
dimension. One of the exciting open problems is to show that all finite dimensional algebras of tame representation type have
representation dimension at most 3. We prove that this is true for all domestic weakly symmetric algebras over algebraically
closed fields having simply connected Galois coverings. 相似文献