![Commutative Algebra with a View Toward Algebraic Geometry [bad OCR]](https://s3.refhub.ir/images/thumb/Commutative_Algebra_with_a_View_Toward_Algebr_15774.webp)
- Published Year: 1994
- Page count: 778
- File Size: 33 Mb
- Language: English
- Published by: Springer
- Visited by: 1
- Rating/Review: 4.6
- ISBN: ISBN information not found.
Keywords:
تندتک
در این کانال تلگرام، مسعود بیگی، تجربیات خود را از دنیای تکنولوژی، استارتاپ، کارآفرینی و مدیریت فنی با شما به اشتراک می گذارد
Learn MoreCommutative Algebra with a View Toward Algebraic Geometry [bad OCR]
4.6
Reviews from our users
You Can Ask your questions from this book's AI after Login
Each download or ask from book AI costs 2 points. To earn more free points, please visit the Points Guide Page and complete some valuable actions.Introduction to 'Commutative Algebra with a View Toward Algebraic Geometry [bad OCR]'
Welcome to a journey through the fascinating realms of both commutative algebra and algebraic geometry, two intertwined fields that form the bedrock of much of modern mathematical theory. This book, 'Commutative Algebra with a View Toward Algebraic Geometry [bad OCR]', is designed to bridge these topics, offering readers a rich tapestry of theory, examples, and applications that connect abstract algebraic concepts with geometric intuition.
Detailed Summary of the Book
The book is primarily an introduction to the basic concepts of commutative algebra, yet it seamlessly integrates ideas and tools from algebraic geometry, making it uniquely suited for readers looking to extend their understanding beyond standard algebraic courses. Throughout its chapters, the book emphasizes the connection between algebraic structures and geometric objects, demonstrating how these mathematical fields inform and illuminate each other.
Starting with foundational notions, such as rings, modules, and ideals, the text gradually introduces more sophisticated topics like localization, primary decomposition, and dimension theory. Each concept is carefully illustrated with examples and exercises that both reinforce the theory and highlight its geometric significance. The nuanced discussion of Noetherian rings and the introduction of schemes and varieties capture the essence of modern algebraic geometry as it stands today.
Key Takeaways
- A comprehensive understanding of the principles of commutative algebra, including its fundamental structures and theorems.
- Insight into the deep connections between algebra and geometry, showcased through the lens of algebraic geometry.
- An appreciation of the elegance and power of algebraic techniques in solving geometric problems and vice versa.
- Enhanced problem-solving skills developed through carefully crafted exercises that integrate theory with practical examples.
Famous Quotes from the Book
"In mathematics, the connections between topics often reveal a deeper truth than the topics themselves."
"The geometric perspective enlivened by algebraic rigor offers a fuller picture of the mathematical landscape."
Why This Book Matters
This book stands out in the vast literature of algebraic texts by serving as a crucial connection point between two pivotal mathematical disciplines. By integrating commutative algebra with algebraic geometry, it provides a robust framework for students and researchers to deepen their knowledge and fuel further exploration in both fields. The author's expert interplay of algebraic methods and geometric intuition creates a narrative that is not only informative but also intellectually inspiring.
For students, this book serves as an insightful guide that prepares them for advanced study and research. For educators, it offers a wealth of material suitable for course instruction and curriculum development. For researchers, it provides a fresh perspective on classic problems and proposes new avenues for inquiry. Ultimately, this book affirms the enduring relevance and power of algebra and geometry in understanding the world of mathematics.
Free Direct Download
Get Free Access to Download this and other Thousands of Books (Join Now)
