The Resource Rings and their modules, Paul E. Bland

Rings and their modules, Paul E. Bland

Label
Rings and their modules
Title
Rings and their modules
Statement of responsibility
Paul E. Bland
Creator
Subject
Language
eng
Member of
Cataloging source
DLC
http://library.link/vocab/creatorName
Bland, Paul E
Dewey number
512/.4
Illustrations
illustrations
Index
index present
LC call number
QA247
LC item number
.B545 2011
Literary form
non fiction
Nature of contents
bibliography
Series statement
De Gruyter graduate
http://library.link/vocab/subjectName
  • Rings (Algebra)
  • Modules (Algebra)
Label
Rings and their modules, Paul E. Bland
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Contents
  • Ordinal and Cardinal Numbers
  • Problem Set 5.3
  • 5.4.
  • Quasi-Injective and Quasi-Projective Modules
  • Problem Set 5.4
  • 6.
  • Classical Ring Theory
  • 6.1.
  • Jacobson Radical
  • Problem Set 6.1
  • 6.2.
  • 0.3.
  • Prime Radical
  • Prime Rings
  • Semiprime Rings
  • Problem Set 6.2
  • 6.3.
  • Radicals and Chain Conditions
  • Problem Set 6.3
  • 6.4.
  • Wedderburn--Artin Theory
  • Problem Set 6.4
  • Commutative Diagrams
  • 6.5.
  • Primitive Rings and Density
  • Problem Set 6.5
  • 6.6.
  • Rings that Are Semisimple
  • Problem Set 6.6
  • 7.
  • Envelopes and Covers
  • 7.1.
  • Injective Envelopes
  • 0.4.
  • Problem Set 7.1
  • 7.2.
  • Projective Covers
  • Radical of a Projective Module
  • Semiperfect Rings
  • Perfect Rings
  • Problem Set 7.2
  • 7.3.
  • QI-Envelopes and QP-Covers
  • Quasi-Injective Envelopes
  • Notation and Terminology
  • Quasi-Projective Covers
  • Problem Set 7.3
  • 8.
  • Rings and Modules of Quotients
  • 8.1.
  • Rings of Quotients
  • Noncommutative Case
  • Commutative Case
  • Problem Set 8.1
  • 8.2.
  • Problem Set
  • Modules of Quotients
  • Problem Set 8.2
  • 8.3.
  • Goldie's Theorem
  • Problem Set 8.3
  • 8.4.
  • Maximal Ring of Quotients
  • Problem Set 8.4
  • 9.
  • Graded Rings and Modules
  • 1.
  • 9.1.
  • Graded Rings and Modules
  • Graded Rings
  • Graded Modules
  • Problem Set 9.1
  • 9.2.
  • Fundamental Concepts
  • Graded Direct Products and Sums
  • Graded Tensor Products
  • Graded Free Modules
  • Basic Properties of Rings and Modules
  • Problem Set 9.2
  • 9.3.
  • Graded Projective, Graded Injective and Graded Flat Modules
  • Graded Projective and Graded Injective Modules
  • Graded Flat Modules
  • Problem Set 9.3
  • 9.4.
  • Graded Modules with Chain Conditions
  • Graded Noetherian and Graded Artinian Modules
  • Problem Set 9.4
  • 1.1.
  • 9.5.
  • More on Graded Rings
  • Graded Jacobson Radical
  • Graded Wedderburn--Artin Theory
  • Problem Set 9.5
  • 10.
  • More on Rings and Modules
  • 10.1.
  • Reflexivity and Vector Spaces
  • Problem Set 10.1
  • Rings
  • 10.2.
  • Reflexivity and R-modules
  • Self-injective Rings
  • Kasch Rings and Injective Cogenerators
  • Semiprimary Rings
  • Quasi-Frobenius Rings
  • Problem Set 10.2
  • 11.
  • Introduction to Homological Algebra
  • 11.1.
  • Machine generated contents note:
  • Problem Set 1.1
  • Chain and Cochain Complexes
  • Homology and Cohomology Sequences
  • Problem Set 11.1
  • 11.2.
  • Projective and Injective Resolutions
  • Problem Set 11.2
  • 11.3.
  • Derived Functors
  • Problem Set 11.3
  • 11.4.
  • 1.2.
  • Extension Functors
  • Right Derived Functors of UomR(--, X)
  • Right Derived Functors of UomR(X, --)
  • Problem Set 11.4
  • 11.5.
  • Torsion Functors
  • Left Derived Functors of -- ⊗ R X and X ⊗ R
  • Problem Set 11.5
  • 12.
  • Homological Methods
  • Left and Right Ideals
  • 12.1.
  • Projective and Injective Dimension
  • Problem Set 12.1
  • 12.2.
  • Flat Dimension
  • Problem Set 12.2
  • 12.3.
  • Dimension of Polynomial Rings
  • Problem Set 12.3
  • 12.4.
  • Factor Rings
  • Dimension of Matrix Rings
  • Problem Set 12.4
  • 12.5.
  • Quasi-Frobenius Rings Revisited
  • More on Reflexive Modules
  • Problem Set 12.5
  • Ordinal and Cardinal Numbers
  • Ordinal Numbers
  • Cardinal Numbers
  • Problem Set
  • Problem Set 1.2
  • 1.3.
  • Ring Homomorphisms
  • Problem Set 1.3
  • 1.4.
  • Modules
  • 0.
  • Factor Modules
  • Problem Set 1.4
  • 1.5.
  • Module Homomorphisms
  • Problem Set 1.5
  • 2.
  • Fundamental Constructions
  • 2.1.
  • Direct Products and Direct Sums
  • Direct Products
  • Preliminaries
  • External Direct Sums
  • Internal Direct Sums
  • Problem Set 2.1
  • 2.2.
  • Free Modules
  • Rings with Invariant Basis Number
  • Problem Set 2.2
  • 2.3.
  • Tensor Products of Modules
  • Problem Set 2.3
  • 0.1.
  • 3.
  • Categories
  • 3.1.
  • Categories
  • Functors
  • Properties of Morphisms
  • Problem Set 3.1
  • 3.2.
  • Exact Sequences in ModR
  • Split Short Exact Sequences
  • Classes, Sets and Functions
  • Problem Set 3.2
  • 3.3.
  • Horn and ⊗ as Functors
  • Properties of Horn
  • Properties of Tensor Products
  • Problem Set 3.3
  • 3.4.
  • Equivalent Categories and Adjoint Functors
  • Adjoints
  • Problem Set 3.4
  • Partial Orders and Equivalence Relations
  • 4.
  • Chain Conditions
  • 4.1.
  • Generating and Cogenerating Classes
  • Problem Set 4.1
  • 4.2.
  • Noetherian and Artinian Modules
  • Problem Set 4.2
  • 4.3.
  • Modules over Principal Ideal Domains
  • Zorn's Lemma and Well-Ordering
  • Free Modules over a PID
  • Finitely Generated Modules over a PID
  • Problem Set 4.3
  • 5.
  • Injective, Projective, and Flat Modules
  • 5.1.
  • Injective Modules
  • Injective Modules and the Functor HomR(--, M)
  • Problem Set 5.1
  • 5.2.
  • 0.2.
  • Projective Modules
  • Projective Modules and the Functor HomR(M, --)
  • Hereditary Rings
  • Semihereditary Rings
  • Problem Set 5.2
  • 5.3.
  • Flat Modules
  • Flat Modules and the Functor M ⊗ R
  • Coherent Rings
  • Regular Rings and Flat Modules
Dimensions
24 cm.
Extent
xiii, 452 p.
Isbn
9783110250220
Isbn Type
(alk. paper)
Lccn
2010034731
Other physical details
ill.
System control number
  • (CaMWU)u2194982-01umb_inst
  • 2332677
  • (Sirsi) i9783110250220
  • (OCoLC)660801331
Label
Rings and their modules, Paul E. Bland
Publication
Bibliography note
Includes bibliographical references and index
Contents
  • Ordinal and Cardinal Numbers
  • Problem Set 5.3
  • 5.4.
  • Quasi-Injective and Quasi-Projective Modules
  • Problem Set 5.4
  • 6.
  • Classical Ring Theory
  • 6.1.
  • Jacobson Radical
  • Problem Set 6.1
  • 6.2.
  • 0.3.
  • Prime Radical
  • Prime Rings
  • Semiprime Rings
  • Problem Set 6.2
  • 6.3.
  • Radicals and Chain Conditions
  • Problem Set 6.3
  • 6.4.
  • Wedderburn--Artin Theory
  • Problem Set 6.4
  • Commutative Diagrams
  • 6.5.
  • Primitive Rings and Density
  • Problem Set 6.5
  • 6.6.
  • Rings that Are Semisimple
  • Problem Set 6.6
  • 7.
  • Envelopes and Covers
  • 7.1.
  • Injective Envelopes
  • 0.4.
  • Problem Set 7.1
  • 7.2.
  • Projective Covers
  • Radical of a Projective Module
  • Semiperfect Rings
  • Perfect Rings
  • Problem Set 7.2
  • 7.3.
  • QI-Envelopes and QP-Covers
  • Quasi-Injective Envelopes
  • Notation and Terminology
  • Quasi-Projective Covers
  • Problem Set 7.3
  • 8.
  • Rings and Modules of Quotients
  • 8.1.
  • Rings of Quotients
  • Noncommutative Case
  • Commutative Case
  • Problem Set 8.1
  • 8.2.
  • Problem Set
  • Modules of Quotients
  • Problem Set 8.2
  • 8.3.
  • Goldie's Theorem
  • Problem Set 8.3
  • 8.4.
  • Maximal Ring of Quotients
  • Problem Set 8.4
  • 9.
  • Graded Rings and Modules
  • 1.
  • 9.1.
  • Graded Rings and Modules
  • Graded Rings
  • Graded Modules
  • Problem Set 9.1
  • 9.2.
  • Fundamental Concepts
  • Graded Direct Products and Sums
  • Graded Tensor Products
  • Graded Free Modules
  • Basic Properties of Rings and Modules
  • Problem Set 9.2
  • 9.3.
  • Graded Projective, Graded Injective and Graded Flat Modules
  • Graded Projective and Graded Injective Modules
  • Graded Flat Modules
  • Problem Set 9.3
  • 9.4.
  • Graded Modules with Chain Conditions
  • Graded Noetherian and Graded Artinian Modules
  • Problem Set 9.4
  • 1.1.
  • 9.5.
  • More on Graded Rings
  • Graded Jacobson Radical
  • Graded Wedderburn--Artin Theory
  • Problem Set 9.5
  • 10.
  • More on Rings and Modules
  • 10.1.
  • Reflexivity and Vector Spaces
  • Problem Set 10.1
  • Rings
  • 10.2.
  • Reflexivity and R-modules
  • Self-injective Rings
  • Kasch Rings and Injective Cogenerators
  • Semiprimary Rings
  • Quasi-Frobenius Rings
  • Problem Set 10.2
  • 11.
  • Introduction to Homological Algebra
  • 11.1.
  • Machine generated contents note:
  • Problem Set 1.1
  • Chain and Cochain Complexes
  • Homology and Cohomology Sequences
  • Problem Set 11.1
  • 11.2.
  • Projective and Injective Resolutions
  • Problem Set 11.2
  • 11.3.
  • Derived Functors
  • Problem Set 11.3
  • 11.4.
  • 1.2.
  • Extension Functors
  • Right Derived Functors of UomR(--, X)
  • Right Derived Functors of UomR(X, --)
  • Problem Set 11.4
  • 11.5.
  • Torsion Functors
  • Left Derived Functors of -- ⊗ R X and X ⊗ R
  • Problem Set 11.5
  • 12.
  • Homological Methods
  • Left and Right Ideals
  • 12.1.
  • Projective and Injective Dimension
  • Problem Set 12.1
  • 12.2.
  • Flat Dimension
  • Problem Set 12.2
  • 12.3.
  • Dimension of Polynomial Rings
  • Problem Set 12.3
  • 12.4.
  • Factor Rings
  • Dimension of Matrix Rings
  • Problem Set 12.4
  • 12.5.
  • Quasi-Frobenius Rings Revisited
  • More on Reflexive Modules
  • Problem Set 12.5
  • Ordinal and Cardinal Numbers
  • Ordinal Numbers
  • Cardinal Numbers
  • Problem Set
  • Problem Set 1.2
  • 1.3.
  • Ring Homomorphisms
  • Problem Set 1.3
  • 1.4.
  • Modules
  • 0.
  • Factor Modules
  • Problem Set 1.4
  • 1.5.
  • Module Homomorphisms
  • Problem Set 1.5
  • 2.
  • Fundamental Constructions
  • 2.1.
  • Direct Products and Direct Sums
  • Direct Products
  • Preliminaries
  • External Direct Sums
  • Internal Direct Sums
  • Problem Set 2.1
  • 2.2.
  • Free Modules
  • Rings with Invariant Basis Number
  • Problem Set 2.2
  • 2.3.
  • Tensor Products of Modules
  • Problem Set 2.3
  • 0.1.
  • 3.
  • Categories
  • 3.1.
  • Categories
  • Functors
  • Properties of Morphisms
  • Problem Set 3.1
  • 3.2.
  • Exact Sequences in ModR
  • Split Short Exact Sequences
  • Classes, Sets and Functions
  • Problem Set 3.2
  • 3.3.
  • Horn and ⊗ as Functors
  • Properties of Horn
  • Properties of Tensor Products
  • Problem Set 3.3
  • 3.4.
  • Equivalent Categories and Adjoint Functors
  • Adjoints
  • Problem Set 3.4
  • Partial Orders and Equivalence Relations
  • 4.
  • Chain Conditions
  • 4.1.
  • Generating and Cogenerating Classes
  • Problem Set 4.1
  • 4.2.
  • Noetherian and Artinian Modules
  • Problem Set 4.2
  • 4.3.
  • Modules over Principal Ideal Domains
  • Zorn's Lemma and Well-Ordering
  • Free Modules over a PID
  • Finitely Generated Modules over a PID
  • Problem Set 4.3
  • 5.
  • Injective, Projective, and Flat Modules
  • 5.1.
  • Injective Modules
  • Injective Modules and the Functor HomR(--, M)
  • Problem Set 5.1
  • 5.2.
  • 0.2.
  • Projective Modules
  • Projective Modules and the Functor HomR(M, --)
  • Hereditary Rings
  • Semihereditary Rings
  • Problem Set 5.2
  • 5.3.
  • Flat Modules
  • Flat Modules and the Functor M ⊗ R
  • Coherent Rings
  • Regular Rings and Flat Modules
Dimensions
24 cm.
Extent
xiii, 452 p.
Isbn
9783110250220
Isbn Type
(alk. paper)
Lccn
2010034731
Other physical details
ill.
System control number
  • (CaMWU)u2194982-01umb_inst
  • 2332677
  • (Sirsi) i9783110250220
  • (OCoLC)660801331

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