Smoktunowicz, A.
On some results related to Köthe's conjecture
(pp. 159-170)
A B S T R A C T S
BOOLEAN RINGS THAT ARE BAIRE SPACES
R. G. Haydon
richard.haydon@brasenose.oxford.ac.uk
2000 Mathematics Subject Classification:
06E10, 46B26, 54E52.
Key words:
Strict convexity, subsequential completeness.
Weak completeness properties of Boolean rings are related to the
property of being a Baire space (when suitably topologised) and to
renorming properties of the Banach spaces of continuous functions on the
corresponding Stone spaces.
EQUIVARIANT EMBEDDINGS OF DIFFERENTIABLE SPACES
R. Faro Rivas
rfaro@unex.es,
J. A. Navarro González
navarro@unex.es,
J. B. Sancho de Salas
jsancho@unex.es
2000 Mathematics Subject Classification:
58A40, 22C05.
Key words:
Affine differentiable spaces, actions of compact
Lie groups, differentiable algebras.
Given a differentiable action of a compact Lie group G on
a compact smooth manifold V, there exists [3] a closed embedding of V
into a finite-dimensional real vector space E so that the action of
G on V may be extended to a differentiable linear action (a linear
representation) of G on E. We prove an analogous equivariant embedding
theorem for compact differentiable spaces (¥-standard
in the sense of [6, 7, 8]).
MODELS OF ALTERNATING RENEWAL PROCESS AT DISCRETE TIME
Moussedek Bousseboua,
Fouad Lazhar Rahmani
frahmani@caramail.com
2000 Mathematics Subject Classification:
60K05, 60G10.
Key words:
Time series, alternating renewal process, sojourn time
laws, persistence.
We study a class of models used with success in the modelling of
climatological sequences. These models are based on the notion of renewal.
At first, we examine the probabilistic aspects of these models to afterwards
study the estimation of their parameters and their asymptotical
properties, in particular the consistence and the normality. We will discuss
for applications, two particular classes of alternating renewal processes at
discrete time. The first class is defined by laws of sojourn time that are
translated negative binomial laws and the second class, suggested by Green
is deduced from alternating renewal process in continuous time with sojourn
time laws which are exponential laws with parameters a^{0} and a^{1} respectively.
ON THE 3-COLOURING VERTEX FOLKMAN NUMBER F(2,2,4)
Nedyalko Dimov Nenov
nenov@fmi.uni-sofia.bg
2000 Mathematics Subject Classification:
05C55.
Key words:
vertex Folkman graph, vertex Folkman number.
In this note we prove that F(2,2,4)=13.
GROUPS WITH DECOMPOSABLE SET OF QUASINORMAL SUBGROUPS
M. De Falco
defalco@matna2.dma.unina.it,
F. de Giovanni
degiova@matna2.dma.unina.it,
C. Musella
musella@matna2.dma.unina.it
2000 Mathematics Subject Classification:
20E15.
Key words:
quasinormal subgroup, decomposable ordered set.
A subgroup H of a group G is said to be quasinormal
if HX = XH for all subgroups X of G. In this article groups
are characterized for which the partially ordered set of quasinormal
subgroups is decomposable.
EXAMPLES ILLUSTRATING SOME ASPECTS OF THE WEAK
DELIGNE-SIMPSON PROBLEM
Vladimir Petrov Kostov
kostov@math.unice.fr
2000 Mathematics Subject Classification:
15A30, 20G05.
Key words:
regular linear system, Fuchsian system, monodromy group.
We consider the variety of (p+1)-tuples of matrices A_{j}
(resp. M_{j})
from given conjugacy classes c_{j} Ì
gl(n,C) (resp. C_{j} Ì
GL(n,C)) such that A_{1}+¼+A_{p+1} = 0
(resp. M_{1}¼M_{p+1} = I).
This variety is connected with the
weak Deligne-Simpson problem: give necessary and sufficient conditions on
the choice of the conjugacy classes c_{j} Ì
gl(n,C) (resp. C_{j} Ì GL(n,C))
so that there exist (p+1)-tuples with trivial centralizers of matrices
A_{j} Î c_{j} (resp. M_{j}
Î C_{j}) whose sum equals 0
(resp. whose product equals I). The matrices A_{j}
(resp. M_{j}) are interpreted
as matrices-residua of Fuchsian linear systems (resp. as
monodromy operators of regular linear systems) on Riemann's sphere. We
consider examples of such varieties of
dimension higher than the expected one due to the presence
of (p+1)-tuples with non-trivial centralizers; in one of the examples
the difference between the two dimensions is O(n).
ON SOME RESULTS RELATED TO KÖTHE'S CONJECTURE
Agata Smoktunowicz
agata.smoktunowicz@yale.edu
2000 Mathematics Subject Classification:
16N40, 16-02.
Key words:
associative ring, nil ideal, Jacobson radical.
The Köthe conjecture states that if a ring R has no nonzero nil
ideals then R has no nonzero nil one-sided ideals.
Although for more than 70 years significant progress has been made,
it is still open in general. In this paper we survey some results
related to the Köthe conjecture as well
as some equivalent problems.
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