LECTURES ON ALGEBRA, VOLUME I

“I cannot imagine that any mathematician would read even a few pages of this book without learning something new or seeing a new connection or gaining an insight into something that they thought they already knew. And between those insights and his writing, you will soon find yourself captivated by Abhyankar as well. I recommend that anyone with an interest in algebra find a copy of this book and flip through it.”

“What is the book good for? The book covers a lot of material for several courses like basic commutative algebra, commutative algebra or algebraic geometry, as well as additional material for basic courses in algebra. It might be used as an encyclopedia for commutative ring theory with a view towards algebraic geometry … it might be used as a source for inspiration for additional, interesting themes for courses as mentioned above … It might be recommended to anybody who is willing to see the fascinating, concrete as well as abstract development of algebra during the last centuries, including its applications to algebraic geometry and its potential … It is a consequence of the author's masterpiece to bring together so many aspects of commutative ring theory. All together, it is not a classical textbook in the style ‘groups, rings, fields’. It is a unique, original exposition full of valuable insights.”

“The result is an incomparable new textbook of abstract algebra, complementing the existing literature in a highly interesting, alternative and utmost valuable manner. Also experienced teachers and researchers in the field can profit a great deal from the author's unique textbook.”