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Author: Jesse Elliott Publisher: Springer Nature ISBN: 3030244016 Category : Mathematics Languages : en Pages : 490
Book Description
This book presents a systematic exposition of the various applications of closure operations in commutative and noncommutative algebra. In addition to further advancing multiplicative ideal theory, the book opens doors to the various uses of closure operations in the study of rings and modules, with emphasis on commutative rings and ideals. Several examples, counterexamples, and exercises further enrich the discussion and lend additional flexibility to the way in which the book is used, i.e., monograph or textbook for advanced topics courses.
Author: Wolmer Vasconcelos Publisher: Springer Science & Business Media ISBN: 3540265031 Category : Mathematics Languages : en Pages : 528
Book Description
This book gives an account of theoretical and algorithmic developments on the integral closure of algebraic structures. It gives a comprehensive treatment of Rees algebras and multiplicity theory while pointing to applications in many other problem areas. Its main goal is to provide complexity estimates by tracking numerically invariants of the structures that may occur.
Author: N. Bourbaki Publisher: Springer Science & Business Media ISBN: 3540642390 Category : Mathematics Languages : en Pages : 654
Book Description
This is the softcover reprint of the English translation of 1972 (available from Springer since 1989) of the first 7 chapters of Bourbaki's 'Algèbre commutative'. It provides a very complete treatment of commutative algebra, enabling the reader to go further and study algebraic or arithmetic geometry. The first 3 chapters treat in succession the concepts of flatness, localization and completions (in the general setting of graduations and filtrations). Chapter 4 studies associated prime ideals and the primary decomposition. Chapter 5 deals with integers, integral closures and finitely generated algebras over a field (including the Nullstellensatz). Chapter 6 studies valuation (of any rank), and the last chapter focuses on divisors (Krull, Dedekind, or factorial domains) with a final section on modules over integrally closed Noetherian domains, not usually found in textbooks. Useful exercises appear at the ends of the chapters.
Author: Craig Huneke Publisher: American Mathematical Soc. ISBN: 082180412X Category : Mathematics Languages : en Pages : 152
Book Description
This monograph deals with the theory of tight closure and its applications. The contents are based on ten talks given at a CBMS conference held at North Dakota State University in June 1995.
Author: Daniel Bump Publisher: World Scientific ISBN: 9789810235611 Category : Mathematics Languages : en Pages : 232
Book Description
This is a graduate-level text on algebraic geometry that provides a quick and fully self-contained development of the fundamentals, including all commutative algebra which is used. A taste of the deeper theory is given: some topics, such as local algebra and ramification theory, are treated in depth. The book culminates with a selection of topics from the theory of algebraic curves, including the Riemann-Roch theorem, elliptic curves, the zeta function of a curve over a finite field, and the Riemann hypothesis for elliptic curves.
Author: Ayman Badawi Publisher: Springer ISBN: 9811370281 Category : Mathematics Languages : en Pages : 280
Book Description
This book highlights the contributions of the eminent mathematician and leading algebraist David F. Anderson in wide-ranging areas of commutative algebra. It provides a balance of topics for experts and non-experts, with a mix of survey papers to offer a synopsis of developments across a range of areas of commutative algebra and outlining Anderson’s work. The book is divided into two sections—surveys and recent research developments—with each section presenting material from all the major areas in commutative algebra. The book is of interest to graduate students and experienced researchers alike.
Author: David Eisenbud Publisher: Springer Science & Business Media ISBN: 1461253500 Category : Mathematics Languages : en Pages : 784
Book Description
This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included.
Author: Winfried Bruns Publisher: Springer Science & Business Media ISBN: 0387763562 Category : Mathematics Languages : en Pages : 461
Book Description
This book examines interactions of polyhedral discrete geometry and algebra. What makes this book unique is the presentation of several central results in all three areas of the exposition - from discrete geometry, to commutative algebra, and K-theory.
Author: Craig Huneke
Author: Craig Huneke
Author: Jesse Elliott
Author: Wolmer Vasconcelos
Author: N. Bourbaki
Author: Craig Huneke
Author: Brian Osserman
Author: Daniel Bump
Author: Ayman Badawi
Author: David Eisenbud
Author: Winfried Bruns