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1.
Applying (enriched) categorical structures we define the notion of ordered sheaf on a quantaloid
, which we call ‘
-order’. This requires a theory of semicategories enriched in the quantaloid
, that admit a suitable Cauchy completion. There is a quantaloid
of
-orders and ideal relations, and a locally ordered category
of
-orders and monotone maps; actually,
. In particular is
, with Ω a locale, the category of ordered objects in the topos of sheaves on Ω. In general
-orders can equivalently be described as Cauchy complete categories enriched in the split-idempotent completion of
. Applied to a locale Ω this generalizes and unifies previous treatments of (ordered) sheaves on Ω in terms of Ω-enriched structures.Mathematics Subject Classifications (2000) 06F07, 18B35, 18D05, 18D20. 相似文献
2.
Given any R-semimodule M equipped with a semitopology
we construct an N-protosummation
for M. If
satisfies certain properties, then a similar construction leads to an unconditional N-summation
for M, that is an N-summation for M equipped with the trivial prenorm MD over the N-summation (DN,D) for D. Conversely any N-protosummation
on M gives rise to a topology
. If both
and
satisfy a certain separation property, then
and
form a Galois connection.
Dedicated to my friend and collegue Nico Pumplün on the occasion of his 70th birthdayMathematics Subject Classifications (2000) 16Y60, 54A05. 相似文献
3.
Let
be an epireflective subcategory of the category Top of topological spaces that is not bireflective (e.g., the category of Hausdorff spaces, the category of Tychonoff spaces) and ℬ be a coreflective subcategory of
. Extending the corresponding result obtained for coreflective subcategories of Top we prove that ℬ is hereditary if and only if it is closed under the formation of prime factors. As a consequence we obtain that every hereditary coreflective subcategory ℬ of
containing a non-discrete space is generated by a class of prime spaces and if
is a quotient-reflective subcategory of Top, then the assignment
gives a bijection of the collection of all hereditary coreflective subcategories of Top that contain the class FG of all finitely generated spaces onto the collection of all hereditary coreflective subcategories of
that contain
. Some applications of these results in the categories of Hausdorff spaces, Tychonoff spaces and zero-dimensional Hausdorff spaces are presented.Mathematics Subject Classifications (2000) 18D15, 54B30. 相似文献
4.
In our previous work, we introduced a bijection between the elements of the crystal base of the negative (resp. positive)
part of the quantized universal enveloping algebra
of a Kac–Moody algebra
that are fixed by a diagram automorphism and the elements of the crystal base of the negative (resp. positive) part of the
quantized universal enveloping algebra
of the orbit Lie algebra
of
. In this paper, we prove that this bijection commutes with the *-operation. As an application of this result we show that
there exists a canonical bijection between the elements ℬ0(λ) of the crystal base ℬ(λ) of an extremal weight module of extremal weight λ over
that are fixed by a diagram automorphism and the elements of the crystal base
of an extremal weight module of extremal weight
over
, if the crystal graph of
is connected.
Presented by P. Littelmann
Mathematics Subject Classifications (2000) Primary: 17B37, 17B10; secondary: 81R50. 相似文献
5.
The main result in Cossidente and Siciliano (J. Number Theory, Vol. 99 (2003) pp. 373–382) states that if a Singer subgroup of PGL(3,q) is an automorphism group of a projective, geometric
irreducible, non-singular plane algebraic curve
then either
or
. In the former case
is projectively equivalent to the curve
with equation Xq+1Y+Yq+1+X=0 studied by Pellikaan. Furthermore, the curve
has a very nice property from Finite Geometry point of view: apart from the three distinguished points fixed by the Singer
subgroup, the set of its
-rational points can be partitioned into finite projective planes
. In this paper, the full automorphism group of such curves is determined. It turns out that
is the normalizer of a Singer group in
. 相似文献
6.
This paper deals with a class
of pseudorandom bit generators – modified alternating
–generators. This class is constructed similarly to the class
of alternating step generators. Three subclasses of
are distinguished, namely linear, mixed and nonlinear generators. The main attention is devoted to the subclass
of linear and mixed generators generating periodic sequences with maximal period lengths. A necessary and sufficient condition for all sequences generated by the linear generators of
to be with maximal period lengths is formulated. Such sequences have good statistical properties, such as distribution of zeroes and ones, and large linear complexity. Two methods of cryptanalysis of the proposed generators are given. Finally, three new classes of modified alternating
–generators, designed especially to be more secure, are presented. 相似文献
7.
We show that for a variety
of Heyting algebras the following conditions are equivalent: (1)
is locally finite; (2) the
-coproduct of any two finite
-algebras is finite; (3) either
coincides with the variety of Boolean algebras or finite
-copowers of the three element chain
are finite. We also show that a variety
of Heyting algebras is generated by its finite members if, and only if,
is generated by a locally finite
-algebra. Finally, to the two existing criteria for varieties of Heyting algebras to be finitely generated we add the following
one:
is finitely generated if, and only if,
is residually finite.
Received November 11, 2001; accepted in final form July 25, 2005. 相似文献
8.
D. Jakubíková-Studenovská 《Algebra Universalis》2009,60(2):125-143
In the present paper we prove that the collection of all convexities of partial monounary algebras is finite; namely, it has exactly 23 elements. Further, we show that for
each element there exists a subset of such that is generated by and card .
This work was supported by the Science and Technology Assistance Agency under the contract No. APVT-20-004104. Supported by
Grant VEGA 1/3003/06. 相似文献
9.
Thomas Scanlon 《Inventiones Mathematicae》2006,163(1):191-211
We prove a p-adic version of the André-Oort conjecture for subvarieties of the universal abelian varieties. Let g and n be integers with n≥3 and p a prime number not dividing n. Let R be a finite extension of
, the ring of Witt vectors of the algebraic closure of the field of p elements. The moduli space
of g-dimensional principally polarized abelian varieties with full level n-structure as well as the universal abelian variety
over
may be defined over R. We call a point
R-special if
is a canonical lift and ξ is a torsion point of its fibre. Employing the model theory of difference fields and work of Moonen
on special subvarieties of
, we show that an irreducible subvariety of
containing a dense set of R-special points must be a special subvariety in the sense of mixed Shimura varieties. 相似文献
10.
Yves Felix Jean-Claude Thomas Micheline Vigué-Poirrier 《Publications Mathématiques de L'IHéS》2004,99(1):235-252
Let M be a closed orientable manifold of dimension d and
be the usual cochain algebra on M with coefficients in a field k. The Hochschild cohomology of M,
is a graded commutative and associative algebra. The augmentation map
induces a morphism of algebras
. In this paper we produce a chain model for the morphism I. We show that the kernel of I is a nilpotent ideal and that the image of I is contained in the center of
, which is in general quite small. The algebra
is expected to be isomorphic to the loop homology constructed by Chas and Sullivan. Thus our results would be translated in terms of string homology. 相似文献
11.
Lutz Strüngmann 《Archiv der Mathematik》2006,86(3):193-204
Let R be a unital associative ring and
two classes of left R-modules. In this paper we introduce the notion of a
In analogy to classical cotorsion pairs as defined by Salce [10], a pair
of subclasses
and
is called a
if it is maximal with respect to the classes
and the condition
for all
and
Basic properties of
are stated and several examples in the category of abelian groups are studied.
Received: 17 March 2005 相似文献
12.
Antonio G. García Miguel A. Hernández-Medina 《Mediterranean Journal of Mathematics》2005,2(3):345-356
Let
be a symmetric operator with compact resolvent defined in a Hilbert space
For any fixed
we consider an entire
function Ka which involves the resolvent of
Associated with Ka we obtain, by duality in
a Hilbert space
of entire functions which becomes a De Branges space of entire functions. This property provides a characterization of
regardless of the anti-linear mapping which has
as its range space. There exists also a sampling formula allowing to recover any function in
from its samples at the sequence of eigenvalues of
This work has been supported by the grant BFM2003–01034 from the D.G.I. of the Spanish Ministerio de Ciencia y Tecnología. 相似文献
14.
We define the reduced minimum modulus
of a nonzero element a in a unital C
*-algebra
by
. We prove that
. Applying this result to
and its closed two side ideal
, we get that dist
,
and
for any
if RR
= 0, where
and
is the quotient homomorphism and
. These results generalize corresponding results in Hilbert spaces. 相似文献
15.
Simon M. Goberstein 《Algebra Universalis》2005,53(4):407-432
A partial automorphism of a semigroup S is any isomorphism between its subsemigroups, and the set all partial automorphisms of S with respect to composition is an inverse monoid called the partial automorphism monoid of S. Two semigroups are said to be
if their partial automorphism monoids are isomorphic. A class
of semigroups is called
if it contains every semigroup
to some semigroup from
Although the class of all inverse semigroups is not
we prove that the class of inverse semigroups, in which no maximal isolated subgroup is a direct product of an involution-free periodic group and the two-element cyclic group, is
It follows that the class of all combinatorial inverse semigroups (those with no nontrivial subgroups) is
A semigroup is called
if it is isomorphic or antiisomorphic to any semigroup that is
to it. We show that combinatorial inverse semigroups which are either shortly connected [5] or quasi-archimedean [10] are
To Ralph McKenzieReceived April 15, 2004; accepted in final form October 7, 2004. 相似文献
16.
Let
be a family of unit balls in
with the property that the mutual distances of the centers are at least
. If any n2 members of
have a common line transversal, then
has a line transversal too.
Received: 27 January 2005; revised: 17 October 2005 相似文献
17.
We consider logarithmic connections, on rank n and degree d vector bundles over a compact Riemann surface X, singular over a fixed point x0 ∈ X with residue in the center of
the integers n and d are assumed to be mutually coprime. A necessary and sufficient condition is given for a vector bundle to admit such a logarithmic
connection. We also compute the Picard group of the moduli space of all such logarithmic connections. Let
denote the moduli space of all such logarithmic connections, with the underlying vector bundle being of fixed determinant
L, and inducing a fixed logarithmic connection on the determinant line L. Let
be the Zariski open dense subset parametrizing all connections such that the underlying vector bundle is stable. The space
of all global sections of certain line bundles on
are computed. In particular, there are no nonconstant algebraic functions on
Therefore, there are no nonconstant algebraic functions on
although
is biholomorphic to a representation space which admits nonconstant algebraic functions. The moduli space
admits a natural compactification by a smooth divisor. We investigate numerically effectiveness of this divisor at infinity.
It turns out that the divisor is not numerically effective in general.
Received: March 2004 Revision: May 2004 Accepted: May 2004 相似文献
18.
Rolf Farnsteiner 《Inventiones Mathematicae》2006,166(1):27-94
Given an algebraically closed field k of characteristic p≥3, we classify the finite algebraic k-groups whose algebras of measures afford a principal block of tame representation type. The structure of such a group
is largely determined by a linearly reductive subgroup scheme
of SL(2), with the McKay quiver of
relative to its standard module being the Gabriel quiver of the principal block
. The graphs underlying these quivers are extended Dynkin diagrams of type
or
, and the tame blocks are Morita equivalent to generalizations of the trivial extensions of the radical square zero tame hereditary
algebras of the corresponding type. 相似文献
19.
Hans-Peter Schröcker 《Journal of Geometry》2005,82(1-2):172-187
We study the projective space
of univariate rational parameterized equations of degree d or less in real projective space
The parameterized equations of degree less than d form a special algebraic variety
We investigate the subspaces on
and their relation to rational curves in
give a geometric characterization of the automorphism group of
and outline applications of the theory to projective kinematics. 相似文献
20.
Congruence properties in congruence permutable and in ideal determined varieties, with applications.
C. J. van. Alten 《Algebra Universalis》2005,53(4):433-449
We define a weak version of EDPC (equationally definable principal congruences), called EDPC*, that is shown to be preserved under varietal closure in congruence permutable varieties. We show that if
is a congruence permutable variety generated by a class
then
has EDPC iff
has EDPC* iff
has EDPC*. An equational condition is given which, if satisfied by
implies that
has the CEP (congruence extension property). Similar results are proved for ideal determined varieties. These results are applied to the variety of residuated lattices, with examples.Received January 15, 2004; accepted in final form October 8, 2004. 相似文献