An introduction to module theory / Ibrahim Assem, Flávio U. Coelho.

Format:

Book

Author/Creator:

Assem, Ibrahim, author.

Coelho, Flávio Ulhoa, author.

Series:

Oxford graduate texts in mathematics.

Oxford scholarship online.

Oxford graduate texts in mathematics

Oxford scholarship online

Language:

English

Subjects (All):

Modules (Algebra).

Physical Description:

1 online resource (609 pages)

Edition:

1st ed.

Place of Publication:

Oxford : Oxford University Press, [2024]

Summary:

This textbook is a modern and accessible account of module theory and is intended for a graduate course on the topic. Written by two specialists, it is addressed to graduate students in algebra, or to students who need algebraic tools in their work. It features a large number of examples worked out in detail, figures and exercises.

Contents:

Cover

Title page

Copyright page

Contents

Introduction

I Rings and Algebras

I.1 Introduction

I.2 Rings and modules

I.3 Algebras

I.4 Algebra morphisms

I.5 Principal ideal domains

II Modules

II.1 Introduction

II.2 Modules and submodules

II.3 Module morphisms

II.4 The isomorphism theorems

III Categories and functors

III.1 Introduction

III.2 Categories and functors

III.3 Products and coproducts of modules

III.4 Free modules

IV Abelian categories

IV.1 Introduction

IV.2 Linear and abelian categories

IV.3 Fibered products and amalgamated sums

IV.4 Equivalences and dualities of categories

V Modules over principal ideal domains

V.1 Introduction

V.2 Free modules and torsion

V.3 The structure theorems

V.4 An application: the Jordan form of a matrix

VI Functors between modules

VI.1 Introduction

VI.2 The tensor product of modules

VI.3 Exact functors

VI.4 Projectives, injectives and flats

VII The chain conditions

VII.1 Introduction

VII.2 Artinian and noetherian modules and algebras

VII.3 Decompositions of algebras

VII.4 Composition series

VII.5 Semisimple modules and algebras

VIII Radicals

VIII.1 Introduction

VIII.2 Radical and socle of a module

VIII.3 Radicals of algebras

VIII.4 Indecomposability

VIII.5 The radical of a module category

IX Projectives and quivers

IX.1 Introduction

IX.2 Projective modules over artinian algebras

IX.3 Morita equivalence

IX.4 Bound quiver algebras

X Homology

X.1 Introduction

X.2 Homology and cohomology

X.3 Derived functors

XI Extension and torsion

XI.1 Introduction

XI.2 The extension and torsion functors

XI.3 Exact sequences and extensions

XII Homological dimensions

XII.1 Introduction

XII.2 Homological dimensions of modules.

XII.3 Homological dimensions of algebras

XII.4 Classes of algebras

Bibliography

Index.

Notes:

Includes bibliographical references and index.

Description based on online resource and publisher information; title from PDF title page (viewed on November 8, 2024).

ISBN:

9780198904939

0198904932

9780198904922

0198904924

OCLC:

1467719456