Коммутативная алгебра

Berlin-Heidelberg-New York.: Springer-Verlag. 1974. — 374 p. — TSBN 3-540-06521-0, Français. (Michel André - École Polytechnique Fédérale de Lausanne). L'exemple des groupes discrets et l'exemple des algèbres de Lie le montrent. Il est utile d'associer à une structure algébrique une bonne notion de modules d'homologie et une bonne notion de modules de cohomologie. Ce livre est...

USA.: University of Illinois, 2003. — 104p. English. This is a text for a basic course in commutative algebra, written in accordance with the following objectives. The idea is to help the student reach an advanced level as quickly and efficiently as possible. In Chapter 1, the theory of primary decomposition is developed so as to apply to modules as well as ideals. In Chapter...

Addison-Wesley, 1969. — 138 Pages. This book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of producing a rapid introduction to the subject. It is designed to be read by students who have had a first elementary course in general algebra. On the other hand, it is not intended as a substitute for the more...

Cambridge: Cambridge University Press, 2004. — 264 p. This book is based on lectures by six internationally known experts presented at the 2002 MSRI introductory workshop on commutative algebra. They focus on the interaction of commutative algebra with other areas of mathematics, including algebraic geometry, group cohomology and representation theory, and combinatorics, with...

Springer, 2019. — 280 p. — (Trends in Mathematics). — ISBN: 978-981-13-7027-4. 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...

Cham: Springer Nature Switzerland, 2024. — 387 p. This book provides a first introduction to the fundamental concepts of commutative algebra. What sets it apart from other textbooks is the extensive collection of 400 solved exercises, providing readers with the opportunity to apply theoretical knowledge to practical problem solving, fostering a deeper and more thorough...

CRC Press, Taylor & Francis Group, 2005. — 410 p. – (Lecture Notes in Pure and Applied Mathematics 241). – ISBN13: 978-0-8247-2327-9. The study of nonunique factorizations of elements into irreducible elements in commutative rings and monoids has emerged as an independent area of research only over the last 30 years and has enjoyed a recent flurry of activity and advancement....

Oxford University Press 1998. — 160 p. — ISBN: 0198501447. This book aims to be a concise introduction to topics in commutative algebra, with an emphasis on worked examples and applications. It combines elegant algebraic theory with applications to number theory, problems in classical Greek geometry, and the theory of finite fields which has important uses in other branches of...

Springer, 1995. — 778 p. Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry. The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition, through dimension theory, differentials, homological...

[Marco Fontana, Salah-Eddine Kabbaj, Bruce Olberding, Irena Swanson. (Editors)]. NY.: Springer, 2011. — 500(viii+492) p. — (e-ISBN: 978-1-4419-6990-3), English. Interactive menu. This volume contains a collection of invited survey articles by some of the leading experts in commutative algebra carefully selected for their impact on the field. Commutative algebra is growing very...

Second edition. — Benjamin/Cummings Publishing Co., Inc., Reading, Mass., 1980. — 313 p. — (Mathematics Lecture Note Series, 56). This book, based on the author's lectures at Brandeis University in 1967 and 1968, is designed for use as a textbook on comuttative algebra by sudents of modern algebraic geometry or abstract algebra. Elementary results. Flatness. Associated primes....

Springer-Verlag Berlin Heidelberg 2011, — 259 p. — (Graduate Texts in Mathematics, Vol. 256). — ISBN: 9783642035449 e-ISBN: 9783642035456 This textbook offers a thorough, modern introduction into commutative algebra. It is intented mainly to serve as a guide for a course of one or two semesters, or for self-study. The carefully selected subject matter concentrates on the...

Springer, 2008. — 324 p. — ISBN: 9783540677338, e-ISBN: 9783540706281. Bridges the current gap in the literature between theory and real computation of Groebner bases and their applications. A comprehensive guide to both the theory and practice of computational commutative algebra, ideal for use as a textbook for graduate or undergraduate students. Contains tutorials on many...

Springer, 2005. — 591 p. — ISBN: 3540255273, 9783540255277. The second volume of the authors’ ‘Computational commutative algebra’…covers on its 591 pages a wealth of interesting material with several unexpected applications. … an encyclopedia on computational commutative algebra, a source for lectures on the subject as well as an inspiration for seminars. The text is...

Birkhauser, 1985. — 246 p. This book will be particularly valuable to the American student because it covers material that is not available in any other textbooks or monographs. The subject of the book is not restricted to commutative algebra developed as a pure discipline for its own sake, nor is it aimed only at algebraic geometry where the intrinsic geometry of a general...

Springer Science+Business Media, Dordrecht, 2015. — 1033 p. — (Algebra and Applications 20) — ISBN: 978-94-017-9943-0. Translated from the popular French edition, this book offers a detailed introduction to various basic concepts, methods, principles, and results of commutative algebra. It takes a constructive viewpoint in commutative algebra and studies algorithmic approaches...

ArXiv.org, 2018. — 1058 p. This book is an introductory course to basic commutative algebra with a particular emphasis on finitely generated projective modules, which constitutes the algebraic version of the vector bundles in differential geometry. We adopt the constructive point of view, with which all existence theorems have an explicit algorithmic content. In particular, when...

Springer-Verlag, 1983. — x, 118 p. — (Lecture Notes in Mathematics, 1023). — ISBN 978-3-540-12722-2, 978-3-540-38704-6. Asymptotic prime divisors protagonise a classical area in commutative ring theory and represent the interface of two major ideas in the study of commutative Noetherian rings. The first, the concept of prime divisors, is one of the most valued tools in the...

Cambridge University Press, 1995. — 153 p. In this well-written introduction to commutative algebra, the author shows the link between commutative ring theory and algebraic geometry. In addition to standard material, the book contrasts the methods and ideology of modern abstract algebra with concrete applications in algebraic geometry and number theory. Professor Reid begins...

Cambridge University Press, 2000. — 367 p. This introductory account of commutative algebra is aimed at students with a background only in basic algebra. Professor Sharp's book provides a good foundation from which the reader can proceed to more advanced works in commutative algebra or algebraic geometry. This new edition contains additional chapters on regular sequences and on...

World Scientific, 2011. — 396 p. — ISBN: 9814313610,9789814313612 This textbook, set for a one or two semester course in commutative algebra, provides an introduction to commutative algebra at the postgraduate and research levels. The main prerequisites are familiarity with groups, rings and fields. Proofs are self-contained. The book will be useful to beginners and experienced...

М.: Национальный исследовательский университет "Высшая школа экономики" (НИУ ВШЭ). — 15 с. Цель этих записок - в помощь студентам кратко изложить содержание лекций с 7 по 11, поскольку подход к этим темам в каждой книжке свой. Считается, что материал лекций с 1 по 6 (спектр кольца, нетеровы кольца, кольца частных, целые расширения, лемма о нормализации, теорема Гильберта о...

Перев. с англ. Ю.И. Манина. — М.: Мир, 1972. — 160 с. М. Атья — известный тополог и алгебраист, лауреат филдсовской премии — знаком советскому читателю по русскому переводу его монографии «Лекции по К-теории» («Мир», 1967). «Введение в коммутативную алгебру», написанное им совместно с И. Макдональдом, также основано на курсе лекций. Эта книга отличается исключительно удачным...

Перев. с англ. Ю.И. Манина. — М.: Мир, 1972. — 160 с. М. Атья — известный тополог и алгебраист, лауреат филдсовской премии — знаком советскому читателю по русскому переводу его монографии «Лекции по К-теории» («Мир», 1967). «Введение в коммутативную алгебру», написанное им совместно с И. Макдональдом, также основано на курсе лекций. Эта книга отличается исключительно удачным...

М.: Мир, 1971. — 708 с. Книга входит в завоевавшую мировое признание энциклопедию современной математики «Элементы математики», созданную группой французских ученых, выступающих под коллективным псевдонимом Н. Бурбаки. Все книги этой серии отличаются оригинальностью изложения и высоким научным уровнем Значительная часть их переведена или переводится на русский язык. Настоящая...

Пер. с англ. — М.: Иностранная литература, 1963. — 379 с. Посвящена общей теории коммутативных колец и охватывает, наряду с классическими результатами, многие факты. Исследуются кольца специальных типов: кольца нормирования, кольца полиномов и степенных рядов и локальные кольца.

Перев. с англ. Е.С. Голод, С.П. Дëмушкин, А.Н. Тюрин. — Под ред. А.И. Узкова. — Москва: Иностранная литература, 1963. — 439 с. За последние десятилетия под влиянием ряда разделов современной математики, таких, как алгебраическая геометрия и другие, интенсивно развивалась теория коммутативных колец и полей. Данным разделам алгебры и посвящена эта обстоятельная монография. Во...