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Author: Robert William Stringall
Publisher:
ISBN:
Category : Abelian groups
Languages : en
Pages : 90
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Book Description
Author: Robert William Stringall
Publisher:
ISBN:
Category : Abelian groups
Languages : en
Pages : 90
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Book Description
Author: P.A. Krylov
Publisher: Springer Science & Business Media
ISBN: 9401703450
Category : Mathematics
Languages : en
Pages : 456
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Book Description
Every Abelian group can be related to an associative ring with an identity element, the ring of all its endomorphisms. Recently the theory of endomor phism rings of Abelian groups has become a rapidly developing area of algebra. On the one hand, it can be considered as a part of the theory of Abelian groups; on the other hand, the theory can be considered as a branch of the theory of endomorphism rings of modules and the representation theory of rings. There are several reasons for studying endomorphism rings of Abelian groups: first, it makes it possible to acquire additional information about Abelian groups themselves, to introduce new concepts and methods, and to find new interesting classes of groups; second, it stimulates further develop ment of the theory of modules and their endomorphism rings. The theory of endomorphism rings can also be useful for studies of the structure of additive groups of rings, E-modules, and homological properties of Abelian groups. The books of Baer [52] and Kaplansky [245] have played an important role in the early development of the theory of endomorphism rings of Abelian groups and modules. Endomorphism rings of Abelian groups are much stu died in monographs of Fuchs [170], [172], and [173]. Endomorphism rings are also studied in the works of Kurosh [287], Arnold [31], and Benabdallah [63].
Author: L. Fuchs
Publisher: Elsevier
ISBN: 148328090X
Category : Mathematics
Languages : en
Pages : 369
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Book Description
Abelian Groups deals with the theory of abelian or commutative groups, with special emphasis on results concerning structure problems. More than 500 exercises of varying degrees of difficulty, with and without hints, are included. Some of the exercises illuminate the theorems cited in the text by providing alternative developments, proofs or counterexamples of generalizations. Comprised of 16 chapters, this volume begins with an overview of the basic facts on group theory such as factor group or homomorphism. The discussion then turns to direct sums of cyclic groups, divisible groups, and direct summands and pure subgroups, as well as Kulikov's basic subgroups. Subsequent chapters focus on the structure theory of the three main classes of abelian groups: the primary groups, the torsion-free groups, and the mixed groups. Applications of the theory are also considered, along with other topics such as homomorphism groups and endomorphism rings; the Schreier extension theory with a discussion of the group of extensions and the structure of the tensor product. In addition, the book examines the theory of the additive group of rings and the multiplicative group of fields, along with Baer's theory of the lattice of subgroups. This book is intended for young research workers and students who intend to familiarize themselves with abelian groups.
Author: P. A. Krylov
Publisher:
ISBN: 9789401703468
Category :
Languages : en
Pages : 458
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Book Description
Author: D. M. Arnold
Publisher: Springer
ISBN: 3540392343
Category : Mathematics
Languages : en
Pages : 199
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Book Description
Author: László Fuchs
Publisher: Springer
ISBN: 3319194224
Category : Mathematics
Languages : en
Pages : 762
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Book Description
Written by one of the subject’s foremost experts, this book focuses on the central developments and modern methods of the advanced theory of abelian groups, while remaining accessible, as an introduction and reference, to the non-specialist. It provides a coherent source for results scattered throughout the research literature with lots of new proofs. The presentation highlights major trends that have radically changed the modern character of the subject, in particular, the use of homological methods in the structure theory of various classes of abelian groups, and the use of advanced set-theoretical methods in the study of un decidability problems. The treatment of the latter trend includes Shelah’s seminal work on the un decidability in ZFC of Whitehead’s Problem; while the treatment of the former trend includes an extensive (but non-exhaustive) study of p-groups, torsion-free groups, mixed groups and important classes of groups arising from ring theory. To prepare the reader to tackle these topics, the book reviews the fundamentals of abelian group theory and provides some background material from category theory, set theory, topology and homological algebra. An abundance of exercises are included to test the reader’s comprehension, and to explore noteworthy extensions and related sidelines of the main topics. A list of open problems and questions, in each chapter, invite the reader to take an active part in the subject’s further development.
Author: Irving Kaplansky
Publisher: Courier Dover Publications
ISBN: 0486836452
Category : Mathematics
Languages : en
Pages : 112
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Book Description
This concise monograph presents the theory of infinite abelian groups in a convenient form and helps students acquire some of the techniques used in modern infinite algebra. 1969 edition.
Author: Rüdiger Göbel
Publisher: American Mathematical Soc.
ISBN: 0821851780
Category : Mathematics
Languages : en
Pages : 450
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Book Description
This volume contains the proceedings of a conference on abelian groups held in August 1993 at Oberwolfach. The conference brought together forty-seven participants from all over the world and from a range of mathematical areas. Experts from model theory, set theory, noncommutative groups, module theory, and computer science discussed problems in their fields that relate to abelian group theory. This book provides a window on the frontier of this active area of research.
Author: Bernard Charles
Publisher: Springer Science & Business Media
ISBN: 3642461468
Category : Mathematics
Languages : en
Pages : 356
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Book Description
Liste des participants et des conferences Table des matieres BAER R. Kollineationen primaerer Praemoduln [1] 1 [2] BAER R. Dualisierbare I!oduln und Praemoduln 37 [3] BEAtJ:IOllT R.A. Abelian groups Gwhich satisty G :: G EPK for every direct summand K of G 69 Sous-groupes fonctoriels et topologies [4J CHARLES B. 75 CUTLER D.O.A topology for primary abelian groups 93 [5J [6] FALTINGS K. Automorphismengruppen endlicher abelscher p-gruppen. 101 [7] FUCHS L. Note on purity and algebraic compactness for modules 121 [8] GP. ABE P.J. Der iterierte Ext-Funktor, seine Periodicität und die dadurch definierten Klassen abelscher Gruppen -- 131 The Jacobson radieal of seme endomorphism rings 143 HAIlW F. [9J HAUSEr, J. Autemorphismengesättigte Klassen abzählbarer [1OJ abelschen Gruppen -- 147 [llJ HILL P. and ;mGIBBElI C. Direct sums of countable bToups and gene- lizations -- 183 ImIDI J.J.!. On topologie al methods in abclian groups 207 [12J KOLETTIS G. Homogeneous decomposable modules 223 [13] 'Endemorphism rings of abelian p-groups LIEBERT 11. 239 [14J l·lADER A. Extensions of abelian groups 259 [15J Sur les proprietes universelles des foncteurs HARlU. DA J. [i6J adjoints --.--.- 267 J.lARTY R. Radieal, soele et relativisation 287 [17] Torsion and cotorsion campletions ----------- [18] llIUES R. 301 A note on endanorphism rings of abelian p-groups 305 [19J m. ITUCE R.
Author: László Fuchs
Publisher: American Mathematical Soc.
ISBN: 082185142X
Category : Mathematics
Languages : en
Pages : 408
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Book Description
This collection of research papers is dedicated to the memory of the distinguished algebraist Robert B. Warfield, Jr. Focusing on abelian group theory and noncommutative ring theory, the book covers a wide range of topics reflecting Warfield's interests and includes two articles surveying his contributions to mathematics. Because the articles have been refereed to high standards and will not appear elsewhere, this volume is indispensable to any researcher in noncommutative ring theory or abelian group theory. With papers by some of the major leaders in the field, this book will also be important to anyone interested in these areas, as it provides an overview of current research directions.
