Hwankoo Kim – författare

This book provides an introduction to the foundations and recent developments in commutative algebra. A look at the contents of the first five chapters shows that the topics covered are those usually found in any textbook on commutative algebra. However, this book differs significantly from most commutative algebra textbooks: namely in its treatment of the Dedekind–Mertens formula, the (small) finitistic dimension of a ring, Gorenstein rings, valuation overrings, the valuative dimension, and the Nagata rings. Chapter 6 goes on to present w-modules over commutative rings, as they are most commonly used in torsion theory and multiplicative ideal theory. Chapter 7 deals with multiplicative ideal theory over integral domains. Chapter 8 collects various results of pullbacks, especially Milnor squares and D + M constructions, which are probably the most important example-generating machines. In Chapter 9, coherent rings of finite weak global dimensions are probed, and the local ring of weak global dimension two is elaborated by combining homological tricks and methods of star operation theory. Chapter 10 is devoted to the Grothendieck group of a commutative ring. In particular, the Bass–Quillen problem is discussed. Finally, Chapter 11 introduces relative homological algebra, especially where the related notions of integral domains appearing in classical ideal theory are defined and studied using the class of Gorenstein projective modules. In Chapter 12, in this new edition, properties of cotorsion theories are introduced and show, for any cotorsion pair, how to construct their homology theory. Each section of the book is followed by a selection of exercises of varying difficulty. This book  appeals to a wide readership, from graduate students to academic researchers interested in studying commutative algebra.

This volume contains selected chapters on algebra and related topics presented at the International Conference on Algebra and its Applications, held at the Department of Mathematics, Faculty of Science and Technology, Sidi Mohamed Ben Abdellah University, Fez, Morocco, from 12–15 July 2023, held in honour of Prof. Ayman Badawi and Prof. Abdelmoujib Benkirane. It contains a cross-section of topics in algebra and its applications which contribute to the development of pure and applied algebra. Chapters in the book focus on modern trends and techniques in various branches of pure and applied algebra and highlight their applications in several other branches of mathematics like coding theory, cryptography and graph theory. Covering a broad range of topics in pure and applied algebra, the book will be useful to a wide spectrum of researchers and graduate students in mathematics.