With contributions from over 50 distinguished mathematicians from more than 15 countries, Abelian Groups, Module Theory, and Topology investigates currently popular topics in abelian group theory and provides a solution to a longstanding problem on automorphisms of p-groups ... studies endomorphism rings and automorphism groups of torsion-free modules over PIDs and valuation domains ... highlights dualities between the categories of abstract and topological modules, and analyzes self-dual locally compact abelian groups ... investigates modules related to equivalences and dualities ... explores various classes of rings and commutative rings with Acc for irreducible ideals ... provides new structural results for valuation and Prufer domains, as well as a technique to build Noetherian domains inside an ideal-adic completion ... elucidates applications of Roelke uniformity in the study of the unitary groups of Hilbert spaces ... supplies up-to-date information on building minimal group topologies on semidirect products ... and much more.
Addresses several principal themes, among them dualities, endomorphism rings and automorphism groups of abelian groups or modules, and topology groups. Specific topics include the Lnroth's theorem for some complete valued fields, greatest common divisors generalized, strongly graded co-algebras and crossed coproducts, torsionless modules and rings with finite essential socle, building Noetheian domains inside an ideal-adic completion, the variety of topological groups generated by the class of all Banach spaces, criteria of steadiness, dualities and pure semi-simple rings, suitable sets in products of topological groups and in groups equipped with the Bohr topology, and tilting in module categories. The 33 research articles and four appreciations of Orsatti's contribution to mathematics were among those presented at an international conference in Padua, Italy, for which no date is noted. No index. Annotation c. by Book News, Inc., Portland, Or.
Research articles: Global Krull dimensions and global dual Krull dimension of valuation rings; The Luroth theorem for some complete valued fields; AB-5 for module and ring extensions; Ko of semiartinian unit-regular rings; Idempotents of the class semigroup of a Prufer domain of finite character; Greatest common divisors generalized; Subgroups of the Baer-Specker group with prescribed endomorphism ring and large dual; Isomorphic automorphism groups of torsion-free p-acid modules; A theorem on extensions of bimodules; Communicative rings with acc on irreducible ideals; Self linearly compact rings and dualities; Extensions of compact Abelian groups by discrete ones and their duality theory II; A note on quasi-duality endomorphism, rings of modules whose cardinality is cofinal to Omega; Endomorphism rings and automorphism groups of separable torsionfree modules over valuation domains; Torsionless modules and rings with finite essential socle; Building noetherian domains inside an ideal-adic completion; G-minimal topological groups; An adjointness relation for finite partition lattices; The variety of topological groups generated by the class of all Banach spaces; On thin generating sets in topological groups; Abelian topological groups without irreducible Banach representations; Cyclic modules over end (Vp) whose endomorphism ring is an ultrapower of D; Automorphisms that determine an Abelian p-group; Dualities and pure-semisimple rings; Suitable sets in products of topological groups and in groups equipped with the Bohr topology; On a duality with less than usual reflexive abstract modules; The Roelcke compactification of unitary groups; Tilting in module categories. (Part contents).
Dikran Dikranjan is an Associate Professor in the Dipartimento di Matematica e Informatica, Universitą di Udine, Italy. He is the author or coauthor of over 90 research papers and books on topological groups, modules and rings, and category theory and its applications, including Topological Groups: Characters, Dualities, and Minimal Group Topologies (Marcel Dekker, Inc.). A member of the Italian Mathematical Union, Dr. Dikranjan received the Ph.D. degree (1978) in mathematics from Sofia University, Bulgaria. Luigi Salce is a Professor in the Dipartimento di Matematica Pura ed Applicata, Universitą di Padova, Italy. He is the author, coauthor, editor, or coeditor of over 50 papers and books on abelian groups and module theory, including Modules Over Valuation Domains (Marcel Dekker, Inc.). A member of the Italian Mathematical Union, Dr. Salce received the doctoral degree (1969) in mathematics from the Universitą di Padova, Italy.
