Overview
- Reprint of the 1972 Edition with errata list and later developments
- Includes supplementary material: sn.pub/extras
Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 195)
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Table of contents (10 chapters)
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Front Matter
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General Theory
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Front Matter
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Structure Theory
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Front Matter
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Errata and Comments for Baer ∗-Rings
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Back Matter
Keywords
About this book
Reviews
A.C. Mewborn 1972 in Zentralblatt für Mathematik, 242.Band, p. 97: "This book is a systematic exposition of Baer*-rings, i.e. rings with involution in which every annihilator one-sided ideal is generated by a projection. In some respects it is an extension of I. Kaplansky’s book “Rings of operators” […]. The study of Baer*-rings is motivated primarily by certain kinds of algebras of linear operators on a Hilbert space and by certain aspects of lattice theory. This book has some of the flavor of both of these but the treatment is almost entirely algebraic. Motivating examples from operator algebras are used extensively. The book is divided into three parts. The first part is a general discussion of *-rings with various conditions on the partially ordered set of projections. The second part is devoted to the structure of Baer *-rings, including the decomposition into types (Types I, II, III, and finite and infinite). Part III occupies about one half of the book and is devoted to the study of finite Baer*-rings (x*x=1 implies x x* = 1). Chapter 6 introduces the notion of a dimension function and shows that every finite Baer *-ring satisfying a generalized comparability condition for projections has a unique dimension function. Chapter 7 contains a representation of a finite Baer *-ring as a subdirect product of finite Baer *-factors. The last two chapters are devoted to the construction of a 'regular hull' of a finite Baer *-ring satisfying certain conditions and to the study of matrix rings over Baer *-rings. This book is well-written and suitable for use both as a text and as a reference on the subject of Baer *-rings. It contains a large number of excellent exercises and problems of varying degrees of difficulty, including a number of open problems."
Authors and Affiliations
Bibliographic Information
Book Title: Baer *-Rings
Authors: Sterling K. Berberian
Series Title: Grundlehren der mathematischen Wissenschaften
DOI: https://doi.org/10.1007/978-3-642-15071-5
Publisher: Springer Berlin, Heidelberg
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1972
Hardcover ISBN: 978-3-540-05751-2Published: 14 July 1972
Softcover ISBN: 978-3-662-31253-7Published: 23 August 2014
eBook ISBN: 978-3-642-15071-5Published: 27 October 2010
Series ISSN: 0072-7830
Series E-ISSN: 2196-9701
Edition Number: 1
Number of Pages: XIII, 301
Topics: Algebra