*Editors*: G. Auchmuty (Houston), H. Brezis (Paris), S.S. Chern
(Berkeley), J. Damon (Chapel Hill), L.C. Evans (Berkeley), R.M. Hardt
(Rice), J.A. Johnson (Houston), A. Lelek (Houston), J. Nagata (Osaka), B. H.
Neumann (Canberra), V. Paulsen (Houston), G. Pisier (College Station and
Paris), R. Scott (Houston), S.W. Semmes (Rice), K. Uhlenbeck (Austin)*
Managing Editor*: K. Kaiser (Houston)

**
Dobbs, David E., **Universityof Tennessee, Knoxville, Tennessee
37996-1300.*Going-Down
Rings with Zero-Divisors,
*pp. 1-12.

ABSTRACT. A (commutative) ring R is defined to be a going-down ring in
case R/P is a going-down domain for each minimal prime ideal P of R. Examples of
going-down rings include arbitrary chained rings and arbitrary going-down
domains. It is proved that if 0 is a primary ideal of a ring R (that is, if each
zero-divisor of R is nilpotent), then R is a going-downring if and oly if the
extension R in T satisfies the going-down property for each overring T of R.
Examples are given to show that neither the "if" nor the "only if" implication
is valid if one deletes the hypothesis that 0 is a primary ideal of R.

**
Nachev, Nako A., **University of Plovdiv,4000 Plovdiv, Bulgaria, and **
Mollov, Todor Zh., **University of Plovdiv,4000 Plovdiv, Bulgaria
(mollov@ulcc.uni-plovdiv.bg).*
On the Isomorphism of Semisimple Group Algebras,
*pp. 13-20.

ABSTRACT. Let KG be the group algebra of an abelian p-group G over a
field K of the first kind with respect to p and let H be an abelian p-group.
Berman and Mollov (1986) have given necessary and sufficient conditions, i.e. a
criterion, for the isomorphism of KG and KH as K-algebras when the first Ulm
factor of the group G is a direct sum of cyclic groups. In this paper we give
new and simplified necessary and sufficient conditions for this isomorphism. In
the case when G is a direct sum of cyclic groups we correct an essential
inaccuracy in the original proof of the criterion.

**Hill, Paul, **
Auburn University, Auburn, AL 36849.*
Another Characterization of Totally Projective Groups,
*pp. 21-28.

**
Feigelstock, Shalom,** Bar-Ilan University,Ramat Gan, Israel
(feigel@macs.biu.ac.il).*
Mapping Near-Rings of Abelian Groups,
*pp. 29-32.

ABSTRACT. Let G be an abelian group, and let p be a prime. A mapping f
from G to G is said to be p-homogeneous if f(px)=pf(x) for all x in G. If every
p-homogeneous mapping from G to G is an endomorphism, then G is said to be
p-endomorphal. If the set of all p-homogeneous maps from G to G is a ring under
pointwise addition and multiplication, then G is said to be semi-p-endomorphal.
It is shown that G is p-endomorphal if and only if G is semi-p-endomorphal. The
p-endomorphal groups are described completely.

**Garity, Dennis J., **
Oregon State University, Corvallis, Oregon 97331
(garity@math.orst.edu), **Jubran , Isa S., **SUNY at Cortland, Cortland,
New York 13045
(jubrani@snycorva.cortland.edu), and **Schori, Richard M., **Oregon State
University, Corvallis, Oregon 97331
(schori@math.orst.edu). *
A Chaotic Embedding of the Whitehead Continuum,
*pp. 33-44.

ABSTRACT In this paper we show that the Whitehead continuum in R^{3 }
arises as a chaotic local attractor for a special self-homeomorphism of R^{3}.
This extends work by R. F. Williams(1967), M. Misiureuicz (1985), W.
Szczechla(1989), and M. Barge and J.Martin(1990) on the problem of determining
which subsets of R^{n}arise as such attractors. We show that for a
certain chaotic map h from S^{1 } to S^{1}, there is an
embedding of the inverse limit of the associated inverse system onto the
Whitehead continuum W in R^{3}and a self homeomorphism g of R^{3 }
such that g(W) = W, the restriction of g to W is topologically conjugate to the
map induced on the inverse limit by h, and W is a local attractor for g. Our
techniques can be used to show that other cell-like subsets of R^{3 }
arising as nested intersections of tori in a regular way can be realized as
chaoticlocal attractors.

**Sakai, Masami, **Kanagawa University,
Yokohama, 221 Japan(msakai@cc.kanagawa-u.ac.jp).*
On Spaces with a Star-Countable k-Network,
*pp. 45-56.

ABSTRACT. It is proved that(1) A space X is a k-space with a
star-countablek-network iff X is dominated by a cover of k-and-aleph_{0}-spaces,(2)
Let X be a k-space, then X is the topological sum of aleph_{0}-spaces
iff X has a star-countable k-network and a point-countable cs-network, (3) Every
Frechet space with apoint-countable separable k-network has a star-countable
k-network.

**Illanes, Alejandro, **Instituto de
Matematicas,Circuito Exterior, Ciudad Universitaria, Mexico, 04510
(illanes@gauss.matem.unam.mx).*
Countable Closed Set Aposyndesis and Hyperspaces,
*pp. 57-64.

ABSTRACT. Let X be a continuum. Answering questions by Erik K. Van
Douwen and Jack T. Goodykoontz, Jr., we show that:

(a) Countable closed set
aposyndesis is a Whitney property,

(b) 2^{X} is a closed set
aposyndetic and,

(c) There exists a dendroid Y such that every positive
Whitney level for C(Y) is zero-dimensional aposyndetic but Y is not aposyndetic.

**
Garcia-Ferreira, Salvador **Instituto de Matematicas,Ciudad
Universitaria, Mexico 04510
(sgarcia@servidor.unam.mx),(sgarcia@zeus.ccu.umich.mx),
and **Sanchis, Manuel,**Universidad Jaume I, Campus de PenyetaRoja,
12071, Castellon, Espana(sanchis@mat.uji.es).*
On C-Compact Subsets,
*pp. 65-86.

**
Arhangel'skii, A.V., **Ohio University, Athen, Ohio 45701-2979
(arhangel@bing.math.ohiou.edu), and **Szeptycki, Paul J., **
Ohio University, Athens, Ohio 45701-2979
(szeptyck@bing.math.ohiou.edu).*
Tightness in Compact Subspaces of C _{rho}-Spaces,
*pp. 87-94.

ABSTRACT. We study the question whether compact subsets C

**Koldobsky,
Alexander, **University of Texas at San Antonio,San Antonio, TX 78249
(koldobsk@math.utsa.edu).*
Inverse Formula for the Blaschke-Levy Representation, *
pp. 95-108.

ABSTRACT. We say that an even
continuous function H on the unit sphere S in R^{n} admits the
Blaschke-Levy representation with q>0 if there exists an even function b in L_{1}(S)
so that, for every x in S, H^{q}(x) is equal to the integral over S of
the function |(x,z)|^{q}b(z). This representation has numerous
applications in convex geometry, probability and Banach space theory. In this
paper, we present a simple formula (in terms of the derivatives of H) for
calculating b out of H. This formula leads to new estimates for the sup-norm of
b that can be used in connection with isometric embeddings of normed spaces in L_{q}.

**
Magajna, Bojan, **University of Ljubljana, Jadranska 19, Ljubljana 1000,
Slovenia
(Bojan.Magajna@fmf.uni-lj.si).*
A Transitivity Problem for Completely Bounded Mappings,
*pp. 109-120.

ABSTRACT. Given a von Neumann algebra R with center C and two elements x
and y in R, a necessary and sufficient condition is provided for the existence
of a completely contractive C-module homomorphism f on R (in the weak* closure
of elementary complete contractions) such that f(x)=y. A related question is
studied for general C*-algebras and the result is used to prove a variant of the
Kadison transitivity theorem for Hilbert C*-modules.

**Li Jiankui, **
Hunan Nornal University,Changsha, Hunan 410081, The People's Republic of China.*
Decomposability of Certain Reflexive Algebras,
*pp.121-126.

ABSTRACT. In this paper, we consider that the lattice-theoretic
conditions on a subspace lattice L which imply that alg(L) is strongly
decomposable and discuss the relation both that alg(L) is semisimple and that
alg(L) is strongly decomposable.

**Baker, Richard L., **The
University of Iowa, Iowa City, Iowa 52242(baker@math.uiowa.edu).*
On Certain Banach Limits of Triangular Matrix Algebras,
*pp. 127-142.

ABSTRACT. In this paper we investigate the class of triangular UHF
(TUHF) Banach algebras. The main result is that the super-natural number
associated to a TUHF Banach algebra is an invariant of the algebra,provided that
the algebra satisfies certain local dimensionality conditions.The proof of the
main result uses purely Banach-algebraic methods, and does not employ
*-algebraic devices.

**Botvinnik, Boris, **University of Oregon,
Eugene OR 97403(botvinn@poincare.uoregon.edu),
and **Gilkey, Peter, **University of Oregon, Eugene OR 97403(gilkey@math.uoregon.edu).*
The Gromov-Lawson-Rosenberg Conjecture: The Twisted Case, *
pp. 143-160.

**
Martel, Yvan, **Universite Pierre et Marie Curie 4,place Jussieu, 75252
Paris Cedex 05.*
Uniqueness of Weak Extremal Solutions ofNonlinear Elliptic Problems,
*pp. 161-168.

ABSTRACT. In this paper, we consider a nonlinear elliptic equation in a
smooth bounded domain.The nonlinearity is positive, convex, nondecreasing and
includes a multiplicative parameter. There exists a value of this parameter
which is critical for the existence of a nonnegative weak solution to this
equation. Previous work have shown the existence of at least a nonnegative weak
solution corresonding to this critical parameter. We prove that this extremal
solution is actually the only solution of the equation with the critical
parameter.

**Silverman, Herb, **University of
Charleston,Charleston, SC 29424.*
Integral Means for Univalent Functionswith Negative Coefficients,
*pp. 169-174.

**
Kirk, W.A., **University of Iowa, Iowa City, Iowa 52242, and **
Shin, Sang Sik, **Kyungpook National University,Taegu, Korea.*
Fixed Point Theorems in Hyperconvex Spaces,
*pp. 175-188.

**
Papageorgiou, Nikolaos S., **National Technical University, Zografou
Campus, Athens 15780, Greece, **Papalina, Francesca ** and **
Vercillo, Susanna,** University of Perugia, Perugia 06123, Italy. *
Minimal Solutions of Nonlinear Parabolic Problems withUnilateral Constraints,
*pp. 189-201.

ABSTRACT. In this paper we consider a class of nonlinear parabolic
variational inequalities, we assume that it has an upper solution and we look
for the minimal solution bounded above by the given upper solution. Our approach
uses truncation and penalization techniques, which lead us to an auxiliary
closely related problem. This is transformed to an equivalent abstract
subdifferential evolution equation, which we solve. We then show that these
solutions also solve the original variational inequality and they are bounded
from above by the upper solution. Finally, an application of Zorn's lemma gives
us the desired minimal solution.

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