Electronic  Edition Vol. 23, No. 1, 1997

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 R3 arises as a chaotic local attractor for a special self-homeomorphism of R3. 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 Rnarise as such attractors. We show that for a certain chaotic map h from S1 to S1, there is an embedding of the inverse limit of the associated inverse system onto the Whitehead continuum W in R3and a self homeomorphism g of R3 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 R3 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-aleph0-spaces,(2) Let X be a k-space, then X is the topological sum of aleph0-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) 2X 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 Crho-Spaces, pp. 87-94.
ABSTRACT. We study the question whether compact subsets Cp(X) have countable tightness for X a Lindelof space. A new class of spaces X is defined for which all compact a in Cp(X) have countable tightness. It is open whether this class includes all Lindelof spaces.

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 Rn admits the Blaschke-Levy representation with q>0 if there exists an even function b in L1(S) so that, for every x in S, Hq(x) is equal to the integral over S of the function |(x,z)|qb(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 Lq.

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.
ABSTRACT. Let M be a compact smooth orientable manifold with cyclic fundamental group of dimension m which is at least 5 whose universal cover is spin. We prove that M admits a metric of positive scalar curvature if and only if the A-roof genus of M vanishes; this proves the Gromov Lawson Rosenberg conjecture in this special case. We also show that the eta invariant completely detects certain connective K theory groups.

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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