Editors: H. Amann (Zürich), G. Auchmuty (Houston), D. Bao
(Houston), H. Brezis (Paris), J. Damon (Chapel Hill), K. Davidson (Waterloo), C.
Hagopian (Sacramento), R. M. Hardt (Rice), J. Hausen (Houston), J. A. Johnson
(Houston), J. Nagata (Osaka), V. I. Paulsen (Houston), G. Pisier (College
Station and Paris), S. W. Semmes (Rice)
Managing Editor: K. Kaiser (Houston)
Houston Journal of Mathematics
Contents
Tsiu--Kwen Lee, Department of Mathematics, National Taiwan University,
Taipei 106, TAIWAN (tklee@math.ntu.edu.tw).
Posner's Theorem for (σ, τ)--Derivations and σ--Centralizing Maps,
pp. 309- 320.
ABSTRACT.
We give a characterization of mappings, which are additive modulo
C, σ--centralizing on Lie ideals in a prime ring with extended centroid
C, and then prove Posner's theorem for (σ, τ)--derivations on Lie ideals.
These results give natural generalizations concerning derivations and
centralizing mappings in prime rings.
Rosales, J. C., García-Sánchez, P. A., García-García, J. I.,
Universidad de Granada, Departamento de Álgebra, 18071 Granada, España
(jrosales@ugr.es, pedro@ugr.es, jigg@ugr.es), and Branco, M. B.,
Universidade de Évora, Departamento de Matemática, 7000 Évora, Portugal
(mbb@uevora.pt).
Saturated Numerical Semigroups,
pp. 321-330.
ABSTRACT.
We characterize those subsets of N that are saturated numerical
semigroups. We introduce the concept of SAT system of generators for a
saturated numerical semigroup, and this will enable us to arrange the set of all
saturated numerical semigroups in a binary tree with no leaves.
David F. Anderson, Department of Mathematics, University of Tennessee,
Knoxville, TN 37996, U. S. A. (anderson@math.utk.edu) and Ayman Badawi,
Dept. of Math. & Stat., The American Univ. of Sharjah, P.O.Box 26666, United
Arab Emirates (abadawi@ausharjah.edu
).
On φ-Prüfer Rings and
φ-Bezout Rings, pp. 331-343.
ABSTRACT.
The purpose of this paper is to introduce two new classes of rings that are
closely related to the classes of Prüfer domains and Bezout domains. Let R be a
commutative ring with 1 such that Nil(R) (the ideal of nilpotent elements of R)
is a divided prime ideal of R, T(R) be the total quotient ring of R, and Z(R) be
the set of zerodivisors of R. Then the map phi from T(R) into R_Nil(R) defined
by phi(a/b) = a/b for every a in R and b in R\Z(R) is a ring homomorphism from
T(R) into R_Nil(R), and phi restricted to R is also a ring homomorphism from R
into R_Nil(R) given by phi(x) = x/1 for every x \in R. A nonnil ideal I of R is
said to be phi-invertible if phi(I) is an invertible ideal of phi(R). If every
finitely generated nonnil ideal of R is phi-invertible, then we say that R is a
phi-Prüfer ring. Also, we say that R is a phi-Bezout ring if phi(I) is a
principal ideal of phi(R) for every finitely generated nonnil ideal I of R. We
show that the theories of phi-Prüfer and phi-Bezout rings resemble that of
Prüfer and Bezout domains.
Shane P. Redmond Southeastern Louisiana University, Hammond, LA
70402, (sredmond@selu.edu).
Structure in the Zero-Divisor
Graph of a Non-Commutative Ring,
pp. 345-355.
ABSTRACT.
In a manner analogous to the commutative case, the zero-divisor graph of a
noncommutative ring R can be defined as the directed graph G. It has been shown
that G is not a tournament if R is a finite ring with no nontrivial nilpotent
elements and the graph has more than one vertex. This result is generalized to
an arbitrary ring. This article also shows that G cannot be a network for a
finite ring R. These results are used to determine which directed graphs on 1,
2, or 3 vertices can be realized as G. Finally, it is shown that for a finite
ring R, G has an even number of directed edges.
Hetzel, Andrew J., Department of Mathematics, The University of
Louisiana, 700 University Avenue, Monroe, LA 71209 (hetzel@ulm.edu).
Quasi-Going-up Rings,
pp. 357-392.
ABSTRACT.
We introduce and develop the theory of "quasi-going-up domains,"
a concept dual to going-down domains. By characterizing quasi-going-up domains
as a particular type of going-down domain, we show that, in addition to Prüfer
domains, the pseudo-valuation domains of Hedstrom and Houston are examples of
quasi- going-up domains. We also define and develop the companion notions of
"absolutely quasi-going-up domain" and "universally quasi-going-up domain." Both
turn out to be examples of going-down domains and, in fact, the latter are
precisely the i-domains of Papick. We conclude by defining and exploring
"quasi-going-up rings," a generalization of quasi-going-up domains to the
context of commutative rings with zero-divisors.
Burel, Jean-Marie, Lund University, 22100 Lund, Sweden (jean-marie.burel@math.lu.se).
Almost contact structures and
harmonic maps with minimal fibres, pp. 393-411.
ABSTRACT.
We study a class of maps between almost contact metric manifolds. We
characterize harmonicity in terms of differential forms which allows one to
construct minimal submanifolds. This new approach allows us to reduce the second
order problem of harmonicity to a first order problem. In particular we show
that any map submersive almost everywhere from a 3-manifold to a surface that
commutes with the contact structure on the domain and the complex structure on
the codomain can be rendered harmonic by a suitable choice of the metric.
Kristály, Alexandru and Varga, Csaba, Faculty of Mathematics
and Informatics, Babes-Bolyai University, Cluj-Napoca, Romania
(akristal@math.ubbcluj.ro),
(csvarga@math.ubbcluj.ro)
and Kozma, László, Institute of Mathematics and Informatics, University
of Debrecen, Debrecen, Hungary
(kozma@math.klte.hu).
The Dispersing of Geodesics in
Berwald Spaces of Non-Positive Flag curvature, pp 413-420.
ABSTRACT.
It is proved that a forward complete Berwald space of non-positive
flag curvature is a generalized Busemann's geodesic space of non-positive
curvature: the length of a median line in any geodesic triangle cannot
succeed the half length of the corresponding side.
D. Shakhmatov, Department of Mathematical Sciences, Faculty of Science,
Ehime University, Matsuyama 790--8577, Japan (dmitri@dpc.ehime-u.ac.jp),
M. Tkachenko,
Departamento de Matemáticas, Universidad Autónoma Metropolitana, Av. San Rafael
Atlixco 186, Del. Iztapalapa, C.P. 09340 Mexico D.F., Mexico (mich@xanum.uam.mx), and
R. G. Wilson,
Departamento de Matemáticas, Universidad Autónoma Metropolitana, Av. San Rafael
Atlixco 186, Del. Iztapalapa, C.P. 09340 Mexico D.F., Mexico (rgw@xanum.uam.mx).
Transversal and T1-Independent
Topologies, pp. 421-433.
ABSTRACT.
A pair of T1 topologies on an infinite set is called
T1-independent if their set-theoretic intersection is the
cofinite topology, and transversal if their set-theoretic union generates
the discrete topology. We show that every Hausdorff space admits a transversal
compact Hausdorff topology. Then we apply Booth's Lemma to prove that no
infinite set of cardinality less than continuum admits a pair of T1-independent
Hausdorff topologies. This answers, in a strong form, a question posed by S.
Watson in 1996. It is shown in ZFC that the remainder of the Stone-Cech
compactification of the countable discrete set is a self T1-independent
compact Hausdorff space, but the existence of self T1-independent
compact Hausdorff spaces of cardinality continuum is both consistent with and
independent of ZFC.
Proctor, C. Wayne, Department of Mathematics and Statistics, Stephen
F. Austin State University, Nacogdoches, Texas 75962-3040
(proctor@math.sfasu.edu).
Continuously Ray Extendible
Continua, pp. 435-450.
ABSTRACT.
The class of all continuously ray extendible continua is defined and shown to
contain all continua with zero span and to be a proper subcollection of the
collection of Class W continua.
Song, Yan-Kui, Nanjing University, Nanjing 210093, P.R. China and
Nanjing Normal University, Nanjing 210097, P.R. China
(songyankui@email.njnu.edu.cn), and Shi, Wei-Xue, Nanjing University,
Nanjing 210093, P.R. China (wxshi@nju.edu.cn).
Subspaces of Absolutely
Star-Lindelöf Spaces, pp. 451-457.
ABSTRACT.
In this paper, we consider two questions on absolute star-Lindelöfness and
star-Lindelöfness: (1) Whether every Tychonoff star-Lindelöf space can be
embedded into some Tychonoff absolutely star-Lindelöf space as a closed subspace
or as a closed Gd-subspace;
(2) Characterize the Tychonoff star-Lindelöf spaces which can be embedded as
regular closed subspaces into Tychonoff absolutely star-Lindelöf spaces. We
proved that the answer to the first question is YES in general. For the second
question we give a complete solution.
Yongge Tian, Department of Mathematics and Statistics, Queen's
University, Kingston, Ontario, Canada K7L 3N6 (ytian@mast.queensu.ca).
Rank Equalities for Block Matrices
and Their Moore-Penrose Inverses, pp. 483-510.
ABSTRACT.
We present in this paper a variety of rank formulas for matrix expressions that
involve Moore-Penrose inverses of block matrices, and use them to characterize
various equalities for Moore-Penrose inverses of block matrices.
Stevo Stevic, Matematicki Institut Srpske Akademije Nauka, Knez
Mihailova 35/I, 1000 Beograd, Serbia (sstevic@ptt.yu; sstevo@matf.bg.ac.yu ).
Weighted Integrals for
Polyharmonic Type Functions, pp. 511-521.
ABSTRACT. We show that if a polyharmonic function on
the unit ball belongs to the weighted Bergman space then all weighted
derivations (of any positve order of derivations) belong to the related weighted
Lebesgue space. Also, a similar result in the case of subharmonic type functions
is proved.
F. Cabello and J.M.F. Castillo, Departamento de Matematicas,
Universidad de Extremadura, Avenida de Elvas, 06071 Badajoz, Spain
(fcabello@unex.es), (castillo@unex.es).
Uniform Boundedness and
Twisted Sums of Banach Spaces, pp. 523-536.
ABSTRACT.
We construct a Banach space X admitting an uncomplemented copy of
l1 so that X/l1 = c0.
To do that we study the uniform boundedness principles that arise when one
considers exact sequences of Banach spaces; as well as several elements of
homological algebra applied to the construction of nontrivial twisted sum of
Banach spaces. The combination of both elements allows one to determine the
existence of nontrivial twisted sums for almost all combinations of classical
Banach spaces.
Damir Bakic
and Boris Guljas, University of Zagreb, Department of Mathematics,
10000 Zagreb, Croatia (bakic@math.hr), (guljas@math.hr).
Extensions of Hilbert C*-modules,
pp. 537-558.
ABSTRACT.
Let V be a full Hilbert C*-module over a non unital C*-algebra. Denote by Vd
the Hilbert C*-module over the multiplier algebra M(A) consisting of all
adjointable maps from A to V. Then V can be naturally embedded in Vd as an ideal submodule and
restriction to V gives an isomorphism of C*-algebras of adjointable operators on
Vd and on V. The extended module Vd is the completion of V with
respect to a variant of strict topology and serves as the largest essential
extension of V, thus can be regarded as the Hilbert C*-module version of the
multiplier algebra. The extended module Vd
of the generalized Hilbert space over A is explicitly determined as a Hilbert
C*-module of sequences in M(A) containing the generalized Hilbert space over
M(A).
Vladimir Bolotnikov and Leiba Rodman, Department of
Mathematics, College of William and Mary, P.O. Box 8795, Williamsburg, VA
23187-8795, USA (vladi@math.wm.edu; lxrodm@math.wm.edu).
Remarks on Interpolation in
Reproducing Kernel Hilbert Spaces, pp. 559-576.
ABSTRACT.
An interpolation problem in reproducing kernel Hilbert spaces is formulated and
solved in terms of the minimal solution and the elements of an auxiliary
reproducing kernel Hilbert space, subject to a norm constraint. The scheme is
illustrated with two particular reproducing kernel Hilbert spaces: the Arveson
space and the Bergman space, where the general theorem leads to convenient
parametrizations of the solution sets.
David E. Edmunds, Centre for Mathematical Analysis and Its
Applications, University of Sussex, Falmer, Brighton, BN1 9QH, U. K. and
Ritva Hurri-Syrjanen, Department of Mathematics, P.O. Box 4, FIN-00014
University of Helsinki, Finland. Current address: University of Michigan,
Department of Mathematics, Ann Arbor, MI 48103, USA (ritvahs@umich.edu)
Rellich's theorem in irregular
domains, pp. 577-586.
ABSTRACT.
We give geometric conditions on a domain which are sufficient for Rellich's
theorem to hold on it. Our results complement earlier work on irregular domains,
such as those satisfying a quasihyperbolic boundary condition and 'rooms and
passages'.
Saïma Khenissy, Laboratoire Jacques-Louis Lions, Université Paris VI,
75252 Paris Cedex 05, France and Olivier Rey, Centre de Mathématiques de
l'Ecole Polytechnique, 91128 Palaiseau Cedex, France
(rey@math.polytechnique.fr).
A Criterion for Existence of
Solutions to the Supercritical Bahri-Coron's Problem, pp. 587-613.
ABSTRACT.
We consider a second order Dirichlet elliptic problem with slightly
supercritical nonlinearity, on a smooth and bounded three dimensional domain W.
We prove that nontriviality of the relative homology between the level sets of
some function j in W¥ W, involving the Green's function and its regular part,
implies the existence of a solution to the problem which blows up, as the
nonlinearity goes to critical growth, at two points, which correspond to a
critical point of j.