| 书目名称 | Sheaves of Algebras over Boolean Spaces | | 编辑 | Arthur Knoebel | | 视频video | | | 概述 | Ties together ideas from universal algebra, topology, and category theory.About half of the theorems provided by the author in the book are new.Open problems and research areas are outlined for the re | | 图书封面 |  | | 描述 | .Sheaves of Algebras over Boolean Spaces. comprehensively covers sheaf theory as applied to universal algebra. The text presents intuitive ideas from topology such as the notion of metric space and the concept of central idempotent from ring theory. These lead to the abstract notions of complex and factor element, respectively. Factor elements are defined by identities, discovered for shells for the first time, explaining why central elements in rings and lattices have their particular form. Categorical formulations of the many representations by sheaves begin with adjunctions and move to equivalences as the book progresses, generalizing Stone’s theorem for Boolean algebras..Half of the theorems provided in the text are new; the rest are presented in a coherent framework, starting with the most general, and proceeding to specific applications. Many open problems and research areas are outlined, including a final chapter summarizing applications of sheaves in diverse fields not covered earlier in the book. This monograph is suitable for graduate students and researchers, and it will serve as an excellent reference text for those who wish to learn about sheaves of algebras.. | | 出版日期 | Book 2012 | | 关键词 | Boolean algebras; Boolean spaces; Stone‘s theorem; categorical formulations; central idempotent; commutat | | 版次 | 1 | | doi | https://doi.org/10.1007/978-0-8176-4642-4 | | isbn_ebook | 978-0-8176-4642-4 | | copyright | Springer Science+Business Media, LLC 2012 |
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发表于 2025-3-21 16:18:26
