共查询到20条相似文献,搜索用时 15 毫秒
1.
Gregor Kemper 《manuscripta mathematica》2001,105(1):139-141
Let be a generic polynomial for a group G in the sense that every Galois extension N/L of infinite fields with group G and K≤L is given by a specialization of g(X). We prove that then also every Galois extension whose group is a subgroup of G is given in this way.
Received: 15 January 2001 相似文献
2.
An algebra A over a field k is FCR if every finite dimensional representation of A is completely reducible and the intersection of the kernels of these representations is zero. We give a useful characterization of FCR-algebras and apply this to C *-algebras and to localizations. Moreover, we show that “small” products and sums of FCR-algebras are again FCR. Received: 25 October 2000 相似文献
3.
We show that a finite distributive lattice has the splitting property - every maximal antichain splits into two parts so
that the lattice is the union of the upset of one part and the downset of the other - if and only if it is a Boolean lattice
or is one of three other lattices. We also introduce a measure of "how splitting" a finite distributive lattice is, and investigate
it.
Received June 13, 2001; accepted in final form July 1, 2002. 相似文献
4.
5.
Jolanta Słomińska 《manuscripta mathematica》2001,104(1):21-38
Let ? be a small category. We present some results which describe cohomology groups and homotopy colimits of functors defined
over ? using cohomology groups and homotopy colimits over certain categories associated to functors from ? to posets.
Received: 3 May 1999 相似文献
6.
Benoit Larose 《Algebra Universalis》2003,49(1):107-109
We prove that the order-primal algebra of a non-trivial finite connected poset P generates a minimal variety if and only if P is dismantlable.
Received November 26, 2002; accepted in final form January 24, 2003. 相似文献
7.
8.
Yuriy A. Drozd 《manuscripta mathematica》2001,104(2):239-256
9.
Artūras Dubickas 《Monatshefte für Mathematik》2004,141(2):119-126
We investigate which algebraic numbers can be Mahler measures. Adler and Marcus showed that these must be Perron numbers. We prove that certain integer multiples of every Perron number are Mahler measures. The results of Boyd give some necessary conditions on Perron number to be a measure. These do not include reciprocal algebraic integers, so it would be of interest to find one which is not a Mahler measure. We prove a result in this direction. Finally, we show that for every non-negative integer k there is a cubic algebraic integer having norm 2 such that precisely the kth iteration of its Mahler measure is an integer. 相似文献
10.
Square matrices over a relation algebra are relation algebras in a natural way. We show that for fixed n, these algebras can be characterized as reducts of some richer kind of algebra. Hence for fixed n, the class of n × n matrix relation algebras has a first–order characterization. As a consequence, homomorphic images and proper extensions of
matrix relation algebras are isomorphic to matrix relation algebras.
Received July 18, 2001; accepted in final form April 24, 2002. 相似文献
11.
Olga Sokratova 《Algebra Universalis》2002,48(4):389-398
In this paper we represent a projective semimodule as a retract of a direct sum of its countably generated projective retracts
with zero intersection. A characterization by means of congruences is also given.
Received May 17, 1999; accepted in final form March 13, 2002.
RID="h1"
ID="h1"This research was supported by ESF grant 4912 and the Fulbright Fellow award.?The author would like to thank the referee
for helpful remarks. 相似文献
12.
Ralf Meyer 《Journal of the European Mathematical Society》2001,3(3):269-286
We prove that entire and periodic cyclic cohomology satisfy excision for extensions of bornological algebras with a bounded
linear section. That is, for such an extension we obtain a six term exact sequence in cohomology.
Received December 16, 1999 / final version received April 18, 2001?Published online May 29, 2001 相似文献
13.
R. Nair 《Monatshefte für Mathematik》2001,132(4):341-348
Let ? be a class of real valued integrable functions on [0,1). We will call a strictly increasing sequence of natural numbers
an sequence if for every f in ? we have
almost everywhere with respect to Lebesgue measure. Here, for a real number y we have used to denote the fractional part of y. For a finite set A we use to denote its cardinality. In this paper we show that for strictly increasing sequences of natural numbers and , both of which are sequences for all , if there exists such that
then the sequence of products of pairs of elements in a and b once ordered by size is also an sequence.
(Received 2 March 2000; in revised form 3 January 2001) 相似文献
14.
Let
be a univariate, separable polynomial of degree n with roots x
1,…,x
n
in some algebraic closure
of the ground field
. It is a classical problem of Galois theory to find all the relations between the roots. It is known that the ideal of all
such relations is generated by polynomials arising from G-invariant polynomials, where G is the Galois group of f(Z). Namely: The action of G on the ordered set of roots induces an action on
by permutation of the coordinates and each
defines a relation P − P(x
1,…,x
n
) called a G-invariant relation. These generate the ideal of all relations. In this note we show that the ideal of relations admits an
H-basis of G-invariant relations if and only if the algebra of coinvariants
has dimension ‖G‖ over
. To complete the picture we then show that the coinvariant algebra of a transitive permutation representation of a finite
group G has dimension ‖G‖ if and only if G = Σ
n
acting via the tautological permutation representation. 相似文献
15.
Given a finitely based self-dual variety of lattices, is it definable, modulo lattice theory, by a single self-dual lattice
identity? There are infinitely many examples with “yes” as the answer and infinitely many with “no.”.
Received December 20, 1999; accepted in final form July 11, 2002. 相似文献
16.
This paper is part of our efforts to develop Stein's method beyond uniform bounds in normal approximation. Our main result
is a proof for a non-uniform Berry–Esseen bound for independent and not necessarily identically distributed random variables
without assuming the existence of third moments. It is proved by combining truncation with Stein's method and by taking the
concentration inequality approach, improved and adapted for non-uniform bounds. To illustrate the technique, we give a proof
for a uniform Berry–Esseen bound without assuming the existence of third moments.
Received: 2 March 2000 / Revised version: 20 July 2000 / Published online: 26 April 2001 相似文献
17.
T. N. Venkataramana 《Monatshefte für Mathematik》2002,135(3):221-244
We give a criterion to determine when the cycle class of a locally symmetric subvariety of a compact locally symmetric variety generates a non-trivial module under the action of Hecke operators, and give several examples where this criterion is satisfied.
We also exhibit examples of subvarieties which do generate the trivial module under the action of Hecke operators. We show that all Hodge classes (in degree ) on the locally symmetric variety associated to certain arithmetric subgroups Γ of are algebraic (provided that ).
Received 16 January 2001; in revised form 18 October 2001 相似文献
18.
Every inverse semigroup possesses a natural partial order and therefore convexity with respect to this order is of interest.
We study the extent to which an inverse semigroup is determined by its lattice of convex inverse subsemigroups; that is, if
the lattices of two inverse semigroups are isomorphic, how are the semigroups related? We solve this problem completely for
semilattices and for inverse semigroups in general reduce it to the case where the lattice isomorphism induces an isomorphism
between the semilattices of idempotents of the semigroups. For many inverse semigroups, such as the monogenic ones, this case
is the only one that can occur. In Part II, a study of the reduced case enables us to prove that many inverse semigroups,
such as the free ones, are strictly determined by their lattices of convex inverse subsemigroups, and to show that the answer
obtained here for semilattices can be extended to a broad class of inverse semigroups, including all finite, aperiodic ones.
Received September 24, 2002; accepted in final form December 15, 2002. 相似文献
19.
Michel Talagrand 《Probability Theory and Related Fields》2001,119(2):187-212
We give a completely rigorous proof that the replica-symmetric solution holds at high enough temperature for the random K-sat problem. The most notable feature of this problem is that the order parameter of the system is a function and not a number.
Received: 21 April 1998 / Revised version: 24 April 2000 / Published online: 21 December 2000 相似文献
20.
In this paper, we give sufficient conditions for the existence of (pseudo) weakly conformal and conformal families of measures for fibred systems. We describe a general construction principle for these families, modelled on the one developed by Denker and Urbanski for conformal measures. For those systems that are fibrewise local homeomorphisms, the constructed families are (pseudo) conformal. If a system is, moreover, weakly topologically exact along fibres, then each measure in the associated family is supported on the whole fibre where it is naturally defined.This research was partially supported by NSF Grant DMS 0100078.Received February 4, 2002; in final form October 24, 2002
Published online October 24, 2003 相似文献