Коммутативная алгебра

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...

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....

[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...

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...

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...