The Algebraic Theory of Modular Systems

Many of the ideas introduced by F.S. Macaulay in this classic 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 that were not systematically developed until considerably later in this century. In this reissue, an introduction by Professor Paul Roberts describes the influence of Macaulay's ideas on recent developments in the subject as well as other changes in the field since then. The background to Macaulay's thinking is discussed, and the development of modern theory is outlined.

Remembered today through the term "Cohen-Macaulay ring", Macaulay is less known for pioneering several other ideas, including the concept of the Gorenstein ring and the use of injective modules. The wealth of ideas expounded here over 75 years ago will still be a source of inspiration to all workers in commutative algebra.