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Ordered ∗ -Rings

✍ Scribed by Thomas C Craven; Tara L Smith

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
114 KB
Volume
238
Category
Article
ISSN
0021-8693

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✦ Synopsis

1157᎐2273 has generalized the notion of )-ordering to the setting of a ring with involution. In this paper we analyze the Ž . ways in which a given )-ordering on the set of symmetric elements can be extended to a multiplicatively closed ordering on a larger set of elements. A complete answer is given for Ore domains.

📜 SIMILAR VOLUMES

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This paper reviews the equations ax = c and xb = d from a new perspective by studying them in the setting of associative rings with or without involution. Results for rectangular matrices and operators between different Banach and Hilbert spaces are obtained by embedding the 'rectangles' into rings

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Let D be a division ring with an involution. Assuming that D admits Baer orderings, we can study the Witt group of Hermitian forms over D by observing its image in the ring of continuous functions on the space of orderings. We are led to define a new class of rings which, when viewed in an abstract