Rings, Modules, Algebras, and Abelian Groups

by Facchini; Alberto

• ISBN13: 9780824748074
• ISBN10: 0824748077
• Format: Nonspecific Binding
• Copyright: 2004-01-28
• Publisher: CRC Press

Summary

Rings, Modules, Algebras, and Abelian Groups summarizes the proceedings of a recent algebraic conference held at Venice International University in Italy. Surveying the most influential developments in the field, this reference reviews the latest research on Abelian groups, algebras and their representations, module and ring theory, and topological algebraic structures, and provides more than 600 current references and 570 display equations for further exploration of the topic. It provides stimulating discussions from world-renowned names including Laszlo Fuchs, Robert Gilmer, Saharon Shelah, Daniel Simson, and Richard Swan to celebrate 40 years of study on cumulative rings.

Table of Contents

Preface	iii
Participants to the Conference	ix
Contributors	xvii
Additives Galois Theory of Modules	1	(12)
R. Abraham
P. Schultz
Finitely Generated and Cogenerated QD Groups	13	(14)
U. Albrecht
B. Wickless
Direct Limits of Modules of Finite Projective Dimension	27	(18)
L. Angeleri Hugel
J. Trlifaj
Classification of a Class of Almost Completely Decomposable Groups	45	(10)
E. Blagoveshchenskaya
A Polynomial Ring Sampler	55	(8)
J. W. Brewer
The Picard Group of the Ring of Integer-valued Polynomials on a Valuation Domain	63	(22)
J.-L. Chabert
A Note on Cotilting Modules and Generalized Morita Duality	85	(4)
R. R. Colby
R. Colpi
K. R. Fuller
Dualities Induced by Cotilting Bimodules	89	(14)
R. Colpi
Symmetries and Asymmetries for Cotilting Bimodules	103	(16)
G. D'Este
A Constructive Solution to the Base Change Decomposition Problem in B(1)-groups	119	(14)
C. De Vivo
C. Metelli
On a Property of the Adele Ring of the Rationals	133	(6)
D. Dikranjan
U. Zannier
On Strong Going-between, Going-down, and their Universalizations	139	(10)
D. E. Dobbs
G. Picavet
Factorization of Divisorial Ideals in a Generalized Krull Domain	149	(12)
S. El Baghdadi
Divisorial Multiplication Rings	161	(16)
J. Escoriza
B. Torrecillas
Global Deformations of Lie Algebras	177	(12)
A. Fialowski
Maximal Prime Divisors in Arithmetical Rings	189	(16)
L. Fuchs
W. Heinzer
B. Olberding
On Strongly Flat Modules over Matlis Domain	205	(14)
L. Fuchs
L. Salce
J. Trlifaj
Group Identities on Unit Groups of Group Algebras	219	(10)
A. Giambruno
C. Polcino Milies
Forty Years of Commutative Ring Theory	229	(28)
R. Gilmer
Modules Induced from a Normal Subgroup of Prime Index	257	(14)
S. P. Glasby
Uniquely Transitive Torsion-free Abelian Groups	271	(20)
R. Gobel
S. Shelah
Generalized E-rings	291	(16)
R. Gobel
S. Shelah
L. Strungmann
Butler Modules and Bext	307	(14)
P. Goeters
C. Vinsonhaler
Remarks on the Multiplicative Structure of Certain One-dimensional Integral Domains	321	(12)
F. Halter-Koch
W. Hassler
F. Kainrath
Non-finitely Generated Prime Ideals in Subrings of Power Series Rings	333	(10)
W. Heinzer
C. Rotthaus
S. Wiegand
Rings with Finitely Many Orbits under the Regular Action	343	(6)
Y. Hirano
Projective Covers and Injective Hulls in Abelian Length Categories	349	(4)
O. Kerner
Semigroup Rings that Are Inside Factorial and Their Cale Representation	353	(12)
U. Krause
Reduced Modules	365	(14)
T.-K. Lee
Y. Zhou
The Mori Property in Rings with Zero Divisors	379	(22)
T. G. Lucas
Minimal Prime Ideals and Generalizations of Factorial Domains	401	(10)
P. Malcolmson
F. Okoh
Factorizations of Monic Polynomials	411	(14)
S. McAdam
R. G. Swan
Monotone Complete Ordered Fields, Generalized Power Series, and Integer Parts	425	(6)
M. Moniri
J. S. Eivazloo
On Distance between Finite Rings	431	(6)
L. Oyuntsetseg
T. Sumiyama
Affine Pairs	437	(12)
I. J. Papick
When a Super-decomposable Pure-injective Module over a Serial Ring Exists	449	(16)
G. Puninski
Path Coalgebras of Quivers with Relations and a Tame-wild Dichotomy Problem for Coalgebras	465	(28)
D. Simson
On Central Galois Algebras of a Galois Algebra	493
G. Szeto
Lianyong Xue