| 書目名稱 | Regularity and Substructures of Hom | | 編輯 | Friedrich Kasch,Adolf Mader | | 視頻video | http://file.papertrans.cn/826/825562/825562.mp4 | | 概述 | Readable text with new concepts opening new avenues for research.Old and numerous new results in self-contained form.Results never published in book form.Extension of the well-known and important conc | | 叢書名稱 | Frontiers in Mathematics | | 圖書封面 |  | | 描述 | Regular rings were originally introduced by John von Neumann to clarify aspects of operator algebras ([33], [34], [9]). A continuous geometry is an indecomposable, continuous, complemented modular lattice that is not ?nite-dimensional ([8, page 155], [32, page V]). Von Neumann proved ([32, Theorem 14. 1, page 208], [8, page 162]): Every continuous geometry is isomorphic to the lattice of right ideals of some regular ring. The book of K. R. Goodearl ([14]) gives an extensive account of various types of regular rings and there exist several papers studying modules over regular rings ([27], [31], [15]). In abelian group theory the interest lay in determining those groups whose endomorphism rings were regular or had related properties ([11, Section 112], [29], [30], [12], [13], [24]). An interesting feature was introduced by Brown and McCoy ([4]) who showed that every ring contains a unique largest ideal, all of whose elements are regular elements of the ring. In all these studies it was clear that regularity was intimately related to direct sum decompositions. Ware and Zelmanowitz ([35], [37]) de?ned regularity in modules and studied the structure of regular modules. Nicholson ([26]) | | 出版日期 | Book 2009 | | 關(guān)鍵詞 | Abelian group; algebra; domain decomposition; homomorphism; module category; regular homomorphism | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-7643-9990-0 | | isbn_softcover | 978-3-7643-9989-4 | | isbn_ebook | 978-3-7643-9990-0Series ISSN 1660-8046 Series E-ISSN 1660-8054 | | issn_series | 1660-8046 | | copyright | Birkh?user Basel 2009 |
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