Ideal theory is important not only for the intrinsic interest and purity of its logical structure but because it is a necessary tool in many branches of mathematics. In this introduction to the modern theory of ideals, Professor Northcott assumes a sound background of mathematical theory but no previous knowledge of modern algebra. After a discussion of elementary ring theory, he deals with the properties of Noetherian rings and the algebraic and analytical theories of local rings. In order to give some idea of deeper applications of this theory the author has woven into the connected...
Ideal theory is important not only for the intrinsic interest and purity of its logical structure but because it is a necessary tool in many branches ...
An important part of homological algebra deals with modules possessing projective resolutions of finite length. This goes back to Hilbert??'s famous theorem on syzygies through, in the earlier theory, free modules with finite bases were used rather than projective modules. The introduction of a wider class of resolutions led to a theory rich in results, but in the process certain special properties of finite free resolutions were overlooked. D. A. Buchsbaum and D. Eisenbud have shown that finite free resolutions have a fascinating structure theory. This has revived interest in the simpler...
An important part of homological algebra deals with modules possessing projective resolutions of finite length. This goes back to Hilbert??'s famous t...
Multilinear algebra has important applications in many different areas of mathematics but is usually learned in a rather haphazard fashion. The aim of this book is to provide a readable and systematic account of multilinear algebra at a level suitable for graduate students. Professor Northcott gives a thorough treatment of topics such as tensor, exterior, Grassmann, Hopf and co-algebras and ends each chapter with a section entitled 'Comments and Exercises'. The comments contain convenient summaries and discussion of the content whilst the exercises provide an opportunity to test understanding...
Multilinear algebra has important applications in many different areas of mathematics but is usually learned in a rather haphazard fashion. The aim of...
Based on a series of lectures given at Sheffield during 1971 72, this text is designed to introduce the student to homological algebra avoiding the elaborate machinery usually associated with the subject. This book presents a number of important topics and develops the necessary tools to handle them on an ad hoc basis. The final chapter contains some previously unpublished material and will provide additional interest both for the keen student and his tutor. Some easily proven results and demonstrations are left as exercises for the reader and additional exercises are included to expand the...
Based on a series of lectures given at Sheffield during 1971 72, this text is designed to introduce the student to homological algebra avoiding the el...
A self-contained introduction to the theory of affine algebraic groups for mathematicians with a basic knowledge of communicative algebra and field theory.
A self-contained introduction to the theory of affine algebraic groups for mathematicians with a basic knowledge of communicative algebra and field th...
