# PDF Download: Introduction To Commutative Algebra by Michael Atiyah and Ian Macdonald - A Must-Read for Algebraic Geometry and Number Theory

## Introduction To Commutative Algebra Michael Atiyah Pdf Download

If you are interested in learning more about commutative algebra, one of the branches of abstract algebra that studies commutative rings, their ideals, and modules over such rings, you might want to check out the book Introduction To Commutative Algebra by Michael Atiyah and Ian Macdonald. This book is a classic and widely used textbook that covers the main topics of commutative algebra in a concise and rigorous way. In this article, we will give you some background information on commutative algebra, Michael Atiyah, and his book, as well as show you how to download the book in PDF format for free.

## Introduction To Commutative Algebra Michael Atiyah Pdf Download

## What is commutative algebra?

Commutative algebra, first known as ideal theory, is the branch of algebra that studies commutative rings, their ideals, and modules over such rings. A ring is a set with two operations, usually called addition and multiplication, that satisfy certain properties such as associativity, commutativity, distributivity, and having identity elements. A ring is commutative if both addition and multiplication are commutative, that is, if a + b = b + a and a * b = b * a for any two elements a and b in the ring. An ideal of a ring is a subset that is closed under addition and under multiplication by any element of the ring. A module over a ring is a generalization of a vector space over a field, where the scalars are replaced by elements of the ring.

### Why is commutative algebra important?

Commutative algebra is important because it provides the foundation for many other areas of mathematics, especially algebraic geometry and algebraic number theory. Algebraic geometry studies geometric objects defined by polynomial equations, such as curves, surfaces, varieties, and schemes. Algebraic number theory studies properties of numbers that can be expressed by polynomial equations with integer coefficients, such as prime numbers, Diophantine equations, and algebraic integers. Both fields use tools and techniques from commutative algebra to study the structure and properties of these objects.

#### Some applications of commutative algebra

One of the most famous applications of commutative algebra is the proof of Fermat's last theorem by Andrew Wiles in 1995. This theorem states that there are no positive integer solutions to the equation x^n + y^n = z^n for any n > 2. Wiles used methods from commutative algebra and modular forms to prove a special case of a conjecture by Barry Mazur and Jean-Pierre Serre, which implied Fermat's last theorem.

Another application of commutative algebra is the classification of finite simple groups by Daniel Gorenstein and others in 1983. This result states that every finite simple group (a group that has no proper normal subgroups) belongs to one of 18 families or is one of 26 exceptional cases. The proof relied on the theory of group representations, which uses commutative algebra to study how groups act on vector spaces.

A third application of commutative algebra is the construction of error-correcting codes by Richard Hamming and others in the 1950s. These codes are used to transmit and store information reliably in the presence of noise and errors. They are based on the idea of adding redundancy to the data by using polynomials over finite fields, which are examples of commutative rings.

## Who is Michael Atiyah?

Michael Atiyah was a British mathematician who made significant contributions to many fields of mathematics, such as topology, geometry, algebra, analysis, and physics. He was born in 1929 in London to a Lebanese father and a Scottish mother. He studied at Cambridge University and Princeton University, where he worked with some of the leading mathematicians of his time, such as John von Neumann, Hermann Weyl, and André Weil. He held professorships at Oxford University, Cambridge University, and the Institute for Advanced Study in Princeton. He died in 2019 at the age of 89.

### His life and achievements

Michael Atiyah was a prolific and influential mathematician who published over 200 papers and books in his career. He received many honors and awards for his work, such as the Fields Medal in 1966, the Abel Prize in 2004, the Copley Medal in 1988, and the Order of Merit in 1992. He was also a leader and promoter of mathematics in the world, serving as the president of the Royal Society, the London Mathematical Society, the International Mathematical Union, and the Royal Society of Edinburgh. He was also involved in many public issues, such as education, science policy, peace, and human rights.

#### His contributions to commutative algebra

One of Michael Atiyah's contributions to commutative algebra was his collaboration with Ian Macdonald on the book Introduction To Commutative Algebra, which was published in 1969. This book is a concise and elegant introduction to the main topics of commutative algebra, such as rings, ideals, modules, localization, Noetherian rings, primary decomposition, Krull dimension, Dedekind domains, valuation rings, integral extensions, and discrete valuation rings. The book is aimed at graduate students and researchers who want to learn the basics of commutative algebra and its applications to algebraic geometry and number theory. The book is widely regarded as a classic and has been used by generations of mathematicians.

Another contribution of Michael Atiyah to commutative algebra was his work on K-theory with Friedrich Hirzebruch in the 1950s and 1960s. K-theory is a branch of algebraic topology that studies topological spaces by using algebraic objects called K-groups. These groups are constructed from vector bundles or modules over rings. K-theory has many applications to geometry, number theory, physics, and other areas of mathematics. Michael Atiyah and Friedrich Hirzebruch developed some of the foundations of K-theory and proved many important results, such as the Atiyah-Hirzebruch spectral sequence, the Atiyah-Singer index theorem, and the Riemann-Roch theorem.

## What is the book Introduction To Commutative Algebra about?

The book Introduction To Commutative Algebra by Michael Atiyah and Ian Macdonald is a textbook that covers the main topics of commutative algebra in a concise and rigorous way. The book consists of eight chapters:

### The main topics covered in the book

The first chapter introduces the basic concepts and definitions of rings, ideals, homomorphisms, quotient rings, operations on ideals, prime ideals, maximal ideals, nilpotent elements, nilradical, Jacobson radical, idempotent elements.

The second chapter introduces modules over a ring, submodules, quotient modules, homomorphisms, exact sequences, direct sums, free modules, finitely generated modules, torsion modules, annihilators, tensor products, localization, flat modules.

The third chapter introduces Noetherian rings, Noetherian modules, Hilbert basis theorem, primary decomposition, associated primes, uniqueness theorem, Lasker-Noether theorem.

The fourth chapter introduces Krull dimension, transcendence degree, Noether normalization lemma, integral dependence, going-up theorem, going-down theorem.

The fifth chapter introduces Dedekind domains, fractional ideals, invertible ideals, ideal class group, unique factorization theorem.

## How to download the book in PDF format?

If you want to read the book Introduction To Commutative Algebra by Michael Atiyah and Ian Macdonald, you might be wondering how to download it in PDF format for free. There are many websites that offer free PDF downloads of books, but not all of them are legal or safe. Some of them might contain viruses, malware, or spyware that can harm your computer or device. Some of them might also violate the copyright of the authors or publishers of the books, which is unethical and illegal.

### The legal and ethical issues of downloading books online

Before you download any book online, you should be aware of the legal and ethical issues involved. Downloading a book without the permission of the author or publisher is considered piracy, which is a form of theft. Piracy deprives the authors and publishers of their rightful income and recognition, and also harms the quality and diversity of literature. Piracy also violates the intellectual property rights of the creators of the books, which are protected by laws such as the Digital Millennium Copyright Act (DMCA) in the United States and the Copyright, Designs and Patents Act (CDPA) in the United Kingdom. If you download a pirated book, you might face legal consequences such as fines, lawsuits, or even criminal charges.

Therefore, you should always respect the rights and wishes of the authors and publishers of the books you want to read. You should only download books from legitimate sources that have obtained the proper licenses or permissions from the copyright holders. You should also avoid sharing or distributing pirated books to others. By doing so, you will support the authors and publishers who create and publish the books you enjoy, and also contribute to the advancement and enrichment of knowledge and culture.

#### The best sources to find the book online

Fortunately, there are some sources that offer free or low-cost access to books online legally and ethically. Some of them are:

Open access platforms: These are platforms that provide free access to academic books and articles that are published under open licenses such as Creative Commons. Some examples are OpenStax , Open Textbook Library , Directory of Open Access Books , Project Gutenberg , Internet Archive , and Google Books . These platforms allow you to read, download, print, or share the books for personal or educational purposes.

Library services: These are services that allow you to borrow or access books from libraries online. Some examples are OverDrive , Libby , Hoopla , and RBdigital . These services require you to have a library card or account from a participating library. You can then browse, borrow, read, or download the books for a limited period of time.

Subscription services: These are services that allow you to access a large collection of books for a monthly or annual fee. Some examples are Scribd , Kindle Unlimited , Audible , and Bookmate . These services require you to create an account and pay a subscription fee. You can then read, listen, or download unlimited books from their catalog.

#### The steps to download the book from a reliable website

As an example, we will show you how to download the book Introduction To Commutative Algebra by Michael Atiyah and Ian Macdonald from Google Books , which is one of the open access platforms mentioned above. Here are the steps:

Go to https://books.google.com/ on your web browser.

Type "Introduction To Commutative Algebra Michael Atiyah" in the search box and press enter.

You will see a list of results related to your search query. Click on the one that matches the title and authors of the book you want.

You will see a preview page of the book with some information such as title, authors, publisher, ISBN, pages, etc. You will also see a button that says "Read" or "Preview". Click on it.

You will see a page that shows some pages of the book that are available for preview. You can scroll through them using the arrows at the bottom.

If you want to download the book in PDF format, you will need to use a tool that can convert the preview pages into a PDF file. One such tool is https://pdfcrowd.com/, which is a free online service that can convert web pages into PDF files. You will need to copy the URL of the preview page and paste it into the box on the website. Then click on "Convert to PDF".

You will see a page that shows the progress of the conversion. When it is done, you will see a button that says "Download PDF". Click on it.

You will see a dialog box that asks you to save the PDF file on your computer or device. Choose a location and a name for the file and click on "Save".

You have successfully downloaded the book in PDF format. You can now open it with any PDF reader or editor of your choice.

## Conclusion

In this article, we have given you some background information on commutative algebra, Michael Atiyah, and his book Introduction To Commutative Algebra. We have also shown you how to download the book in PDF format for free from Google Books. We hope you have enjoyed reading this article and learned something new and useful. If you want to learn more about commutative algebra, we recommend you to read the book by Atiyah and Macdonald, as well as other books and resources on the subject.

## FAQs

Q: What is commutative algebra?

A: Commutative algebra is the branch of algebra that studies commutative rings, their ideals, and modules over such rings.

Q: Who is Michael Atiyah?

A: Michael Atiyah was a British mathematician who made significant contributions to many fields of mathematics, such as topology, geometry, algebra, analysis, and physics.

Q: What is the book Introduction To Commutative Algebra about?

A: The book Introduction To Commutative Algebra by Michael Atiyah and Ian Macdonald is a classic and widely used textbook that covers the main topics of commutative algebra in a concise and rigorous way.

Q: How to download the book in PDF format?

A: You can download the book in PDF format for free from Google Books by following the steps described in this article.

Q: What are some applications of commutative algebra?

A: Some applications of commutative algebra are the proof of Fermat's last theorem, the classification of finite simple groups, and the construction of error-correcting codes.

71b2f0854b