The Algebraic Theory of Modular Systems

Many of the ideas introduced by Macaulay in this book have developed into central concepts in what has become the branch of mathematics known as Commutative Algebra. Today his name is remembered through the term ‘Cohen–Macaulay ring’, however, it is less well known that he pioneered several other fundamental ideas, including the concept of the Gorenstein ring and the use of injective modules, ideas which were not systematically developed until considerably later in this century. An introduction by Professor Paul Roberts links past with present. The background to Macaulay’s thinking is discussed, and the development of modern theory is outlined. The wealth of ideas expounded here by Macaulay over 75 years ago, will still be a source of inspiration to all workers in commutative algebra.