Basic Algebra: Groups, Rings and Fields

ISBN-13: 9781447110606 / Angielski / Miękka / 2012 / 465 str.

Paul M. Cohn

Opis

This is the first volume of a revised edition of P.M. Cohn's classic three-volume text Algebra, widely regarded as one of the most outstanding introductory algebra textbooks. This volume covers the important results of algebra. Readers should have some knowledge of linear algebra, groups and fields, although all the essential facts and definitions are recalled.

Recenzje

From the reviews:

"The book is a wonderful piece of work that condenses and transmits the long experience of an excellent teacher. The reader enjoys the structure of the precisely designed volume and the beautiful combination of clear arguments and well-chosen examples. A lot of exercises help the reader to deepen his knowledge. This updated and improved introduction to abstract algebra must be on the bookshelves of all algebraists and of all students interested in algebra." (Maria B. Szendrei, Acta Scientiarum Mathematicarum, Vol. 71, 2005)

"This is a coherent overview of group, ring and field theory which combines brevity with elegance and authority. ... to the serious algebraists and departmental libraries ... this book will be an automatic purchase." (Gerry Leversha, The Mathematical Gazette, March, 2005)

"This book ... is a new and revised version of the author's famous text 'Algebra' ... . The book contains numerous exercises, and ... many illuminating comments on the subject. There is no doubt that the book will take the position of its predecessor in being one of the most outstanding introductory algebra textbooks." (EMS Newsletter, June, 2004)

"The entire text is profusely supported by worked examples. Each section in the book comes with a plentiful supply of carefully selected exercises, and there are also numerous historical remarks and hints for further reading. Altogether, this textbook breathes once more the author's rich teaching experience and his masterly skill as a textbook writer. ... the author has kept his well-tried methodical principle of combining old and new viewpoints in algebra in a natural way, which makes his textbooks so unique, matchless and timelessly valuable." (Werner Kleinert, Zentralblatt MATH, Vol. 1003 (3), 2003)

Spis treści

Preface.- Conventions on Terminology.- Sets.- Groups.- Lattices and Categories.- Rings and Modules.- Algebras.- Multilinear Algebra.- Field Theory.- Quadratic Forms and Ordered Fields.- Valuation Theory.- Commutative Rings.- Infinite Field Extensions.- Bibliography.- List of Notations.- Author Index.- Subject Index.