Formal matrices. (2017)

• Record Type: Book
• Further Information: Note: Piotr Krylov, Askar Tuganbaev.
• Authors: Krylov, Piotr A; Tuganbaev, Askar A
• Contents: Symbols; 1 Introduction; 2 Formal Matrix Rings; 2.1 Construction of Formal Matrix Rings of Order 2; 2.2 Examples of Formal Matrix Rings of Order 2; 2.3 Formal Matrix Rings of Order nge2; 2.4 Some Ideals of Formal Matrix Rings; 2.5 Ring Properties; 2.6 Additive Problems; 3 Modules over Formal Matrix Rings; 3.1 Initial Properties of Modules over Formal Matrix Rings; 3.2 Small and Essential Submodules; 3.3 The Socle and the Radical; 3.4 Injective Modules and Injective Hulls; 3.5 Maximal Rings of Fractions; 3.6 Flat Modules; 3.7 Projective and Hereditary Modules and Rings. 3.8 Equivalences Between the Categories R-Mod, S-Mod, and K-Mod3.9 Hereditary Endomorphism Rings of Abelian Groups; 4 Formal Matrix Rings over a Given Ring; 4.1 Formal Matrix Rings over a Ring R; 4.2 Some Properties of Formal Matrix Rings over R; 4.3 Characterization of Multiplier Matrices; 4.4 Classification of Formal Matrix Rings; 4.5 The Isomorphism Problem; 4.6 Determinants of Formal Matrices; 4.7 Some Theorems About Formal Matrices; 5 Grothendieck and Whitehead Groups of Formal Matrix Rings; 5.1 Equivalence of Two Categories of Projective Modules; 5.2 The Group K0(A, B). 5.3 K0 Groups of Formal Matrix Rings5.4 The K1 Group of a Formal Matrix Ring; 5.5 K0 and K1 Groups of Matrix Rings of Order nge2; References ; Index.
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2017
• Extent: 1 online resource
• Subjects: 512.9/434; 510; Mathematics; Matrices; MATHEMATICS -- Matrices; Matrices; Mathematics -- Algebra -- Abstract; Mathematics -- Algebra -- Linear; Mathematical foundations; Algebraic topology; Algebra; Algebra; Matrix theory; Electronic books
• Languages: English
• ISBNs: 9783319539072; 3319539078
• Related ISBNs: 9783319539065; 331953906X
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (SpringerLink, viewed April 10, 2017).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.