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" Cyclic modules and the structure of rings / "
by S.K. Jain, Ashish K. Srivastava, Askar A. Tuganbaev
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BL
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| Record Number
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624584
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dltt
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| Main Entry
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Jain, S. K.
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| Title & Author
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Cyclic modules and the structure of rings /\ by S.K. Jain, Ashish K. Srivastava, Askar A. Tuganbaev
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| Series Statement
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Oxford mathematical monographs
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| Page. NO
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1 online resource
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| ISBN
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9780191641541
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: 0191641545
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: 6613951994
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: 9786613951991
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: 9781283639538
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: 128363953X
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: 9780191746024
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: 0191746029
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9780199664511
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019966451X
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| Bibliographies/Indexes
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Includes bibliographical references and index
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| Contents
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""Cover""; ""Contents""; ""1 Preliminaries""; ""1.1 Artinian and noetherian modules""; ""1.2 Free modules, projective modules, and injective modules""; ""1.3 Hereditary and semihereditary rings""; ""1.4 Generalizations of injectivity""; ""2 Rings characterized by their proper factor rings""; ""2.1 Restricted artinian rings""; ""2.2 Restricted perfect rings""; ""2.3 Restricted von Neumann regular rings""; ""2.4 Restricted self-injective rings""; ""3 Rings each of whose proper cyclic modules has a chain condition""; ""3.1 Rings each of whose proper cyclic modules is artinian""
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""3.2 Rings with restricted minimum condition""""3.3 Rings each of whose proper cyclic modules is perfect""; ""4 Rings each of whose cyclic modules is injective (or CS)""; ""4.1 Rings where each cyclic module is injective""; ""4.2 Rings each of whose cyclic modules is CS""; ""5 Rings each of whose proper cyclic modules is injective""; ""6 Rings each of whose simple modules is injective (or [Sigma]-injective)""; ""6.1 V -rings""; ""6.2 WV-rings""; ""6.3 [Sigma]-V rings""; ""6.4 CSI rings""; ""7 Rings each of whose (proper) cyclic modules is quasi-injective""
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""7.1 Rings each of whose cyclic modules is quasi-injective""""7.2 Rings each of whose proper cyclic modules is quasi-injective""; ""8 Rings each of whose (proper) cyclic modules is continuous""; ""8.1 Rings each of whose cyclic modules is continuous""; ""8.2 Rings each of whose proper cyclic modules is continuous""; ""9 Rings each of whose (proper) cyclic modules is [pi]-injective""; ""9.1 Rings each of whose cyclic modules is [pi]-injective""; ""9.2 Rings each of whose proper cyclic modules is [pi]-injective""
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""10 Rings with cyclics N[sub(0)]-injective, weakly injective, or quasi-projective""""10.1 Rings each of whose cyclic modules is N[sub(0)]-injective""; ""10.2 Rings each of whose cyclic modules is weakly injective""; ""10.3 Rings each of whose cyclic modules is quasi-projective""; ""11 Hypercyclic, q-hypercyclic, and [pi]-hypercyclic rings""; ""11.1 Hypercyclic rings""; ""11.2 q-hypercyclic rings""; ""11.3 [pi]-hypercyclic rings""; ""12 Cyclic modules essentially embeddable in free modules""; ""13 Serial and distributive modules""
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""14 Rings characterized by decompositions of their cyclic modules""""15 Rings each of whose modules is a direct sum of cyclic modules""; ""16 Rings each of whose modules is an I[sub(0)]-module""; ""17 Completely integrally closed modules and rings""; ""18 Rings each of whose cyclic modules is completely integrally closed""; ""19 Rings characterized by their one-sided ideals""; ""19.1 Rings each of whose one-sided ideals is quasi-injective""; ""19.2 Rings each of whose one-sided ideals is a direct sum of quasi-injectives""; ""19.3 Rings each of whose one-sided ideals is [pi]-injective""
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| Abstract
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This unique and comprehensive volume provides an up-to-date account of the literature on the subject of determining the structure of rings over which cyclic modules or proper cyclic modules have a finiteness condition or a homological property. The finiteness conditions and homological properties are closely interrelated in the sense that either hypothesis induces the other in some form. This is the first book to bring all of this important material on the subject together. Over the last 25 years or more numerous mathematicians have investigated rings whose factor rings or factor modules have a finiteness condition or a homological property. They made important contributions leading to new directions and questions, which are listed at the end of each chapter for the benefit of future researchers. There is a wealth of material on the topic which is combined in this book, it contains more than 200 references and is not claimed to be exhaustive. This book will appeal to graduate students, researchers, and professionals in algebra with a knowledge of basic noncommutative ring theory, as well as module theory and homological algebra, equivalent to a one-year graduate course in the theory of rings and modules
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| Subject
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Noncommutative rings
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Artin rings
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Commutative rings
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Noetherian rings
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| Dewey Classification
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512.4
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| LC Classification
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QA251.4
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| Added Entry
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Srivastava, Ashish K.
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Tuganbaev, Askar A.
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