The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth century. This is the second volume of Algebras, Rings and Modules: Non-commutative Algebras and Rings by M. Hazewinkel and N. Gubarenis, a continuation stressing the more important recent results on advanced topics of the structural theory of associative algebras, rings and modules.

Extending modules are generalizations of injective modules and, dually, lifting modules generalize projective supplemented modules. This duality exhibits a certain asymmetry. While the theory of extending modules is well documented in monographs and text books, the purpose of this monograph is to provide a thorough study of supplements and projectivity conditions needed to investigate classes of modules related to lifting modules.

This monograph is concerned with exchange rings in various conditions related to stable range. Diagonal reduction of regular matrices and cleanness of square matrices are also discussed. Readers will come across various topics: cancellation of modules, comparability of modules, cleanness, monoid theory, matrix theory, K-theory, topology, amongst others. This is a first-ever book that contains many of these topics considered under stable range conditions. It will be of great interest to researchers and graduate students involved in ring and module theories.

Being Reconciled is a radical and entirely fresh theological treatment of the classic theory of the Gift in the context of divine reconciliation. It reconsiders notions of freedom and exchange in relation to a Christian doctrine which understands Creation, grace and incarnation as heavenly gifts, but the Fall, evil and violence as refusal of those gifts. In a sustained and rigorous response to the works of Derrida, Levinas, Marion, Zizek, Hauerwas and the 'Radical Evil' school, John Milbank posits the daring view that only transmission of the forgiveness offered by the Divine Humanity makes reconciliation possible on earth. Any philosophical understanding of forgiveness and redemption therefore requires theological completion. Both a critique of post-Kantian modernity, and a new theology that engages with issues of language, culture, time, politics and historicity, Being Reconciled insists on the dependency of all human production and understanding on a God who is infinite in both utterance and capacity. Intended as the first in a trilogy of books centred on the gift, this book is an original and vivid new application of a classic theory by a leading international theologian.

This book gives an introduction to functional analysis in a way that is tailored to fit the needs of the researcher or student. The book explains the basic results of functional analysis as well as relevant topics in numerical analysis. Applications of functional analysis are given by considering numerical methods for solving partial differential equations and integral equations. The material is especially useful for researchers and students who wish to work in theoretical numerical analysis and seek a background in the "tools of the trade" covered in this book.

The Handbook on the Economics of Giving, Reciprocity and Altruism provides a comprehensive set of reviews of literature on the economics of nonmarket voluntary transfers. The foundations of the field are reviewed first, with a sequence of chapters that present the hard core of the theoretical and empirical analyses of giving, reciprocity and altruism in economics, examining their relations with the viewpoints of moral philosophy, psychology, sociobiology, sociology and economic anthropology. Secondly, a comprehensive set of applications are considered of all the aspects of society where nonmarket voluntary transfers are significant: family and intergenerational transfers; charity and charitable institutions; the nonprofit economy; interpersonal relations in the workplace; the Welfare State; and international aid.*Every volume contains contributions from leading researchers*Each Handbook presents an accurate, self-contained survey of a particular topic *The series provides comprehensive and accessible surveys

The concept of surplus captures the politics of production and also conveys the active material means by which people develop the strategies to navigate everyday life. Surplus: The Politics of Production and the Strategies of Everyday Life examines how surpluses affected ancient economies, governments, and households in civilizations across Mesoamerica, the Southwest United States, the Andes, Northern Europe, West Africa, Mesopotamia, and eastern Asia. A hallmark of archaeological research on sociopolitical complexity, surplus is central to theories of political inequality and institutional finance. This book investigates surplus as a macro-scalar process on which states or other complex political formations depend and considers how past people—differentially positioned based on age, class, gender, ethnicity, role, and goal—produced, modified, and mobilized their social and physical worlds. Placing the concept of surplus at the forefront of archaeological discussions on production, consumption, power, strategy, and change, this volume reaches beyond conventional ways of thinking about top-down or bottom-up models and offers a comparative framework to examine surplus, generating new questions and methodologies to elucidate the social and political economies of the past. Contributors include Douglas J. Bolender, James A. Brown, Cathy L. Costin, Kristin De Lucia, Timothy Earle, John E. Kelly, Heather M. L. Miller, Christopher R. Moore, Christopher T. Morehart, Neil L. Norman, Ann B. Stahl, Victor D. Thompson, T. L. Thurston, and E. Christian Wells.