Автор: Tercan Название: Module Theory, Extending Modules and Generalizations ISBN: 3034809506 ISBN-13(EAN): 9783034809504 Издательство: Springer Рейтинг: Цена: 15372.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The main focus of this monograph is to offer a comprehensive presentation of known and new results on various generalizations of CS-modules and CS-rings. Extending (or CS) modules are generalizations of injective (and also semisimple or uniform) modules. While the theory of CS-modules is well documented in monographs and textbooks, results on generalized forms of the CS property as well as dual notions are far less present in the literature.With their work the authors provide a solid background to module theory, accessible to anyone familiar with basic abstract algebra. The focus of the book is on direct sums of CS-modules and classes of modules related to CS-modules, such as relative (injective) ejective modules, (quasi) continuous modules, and lifting modules. In particular, matrix CS-rings are studied and clear proofs of fundamental decomposition results on CS-modules over commutative domains are given, thus complementing existing monographs in this area.Open problems round out the work and establish the basis for further developments in the field. The main text is complemented by a wealth of examples and exercises.
Автор: Chazal Название: The Structure and Stability of Persistence Modules ISBN: 3319425439 ISBN-13(EAN): 9783319425436 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This book is a comprehensive treatment of the theory of persistence modules over the real line. It presents a set of mathematical tools to analyse the structure and to establish the stability of such modules, providing a sound mathematical framework for the study of persistence diagrams. Completely self-contained, this brief introduces the notion of persistence measure and makes extensive use of a new calculus of quiver representations to facilitate explicit computations.
Appealing to both beginners and experts in the subject, The Structure and Stability of Persistence Modules provides a purely algebraic presentation of persistence, and thus complements the existing literature, which focuses mainly on topological and algorithmic aspects.
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