Publication: A partial order on subsets of baer bimodules with applications to c*-modules
No Thumbnail Available
Date
2021-11-01
Authors
Authors
Birkenmeier, Gary F.
Kara, Yeliz
Journal Title
Journal ISSN
Volume Title
Publisher
World Scientific Publ Co Pte Ltd
Abstract
In this paper, we introduce the concept of Baer (p, q)-sets. Using this notion, we define Rickart, Baer, quasi-Baer and pi-Baer (S, R)-bimodules, respectively. We show how these conditions relate to each other. We also develop new properties of the minus binary relation, <=-, we extend the relation <=- to (S, R)-bimodules and use it to characterize the aforementioned Rickart, Baer, quasi-Baer, and pi-Baer (S,R)-bimodules. Moreover, we specify subsets kappa of the power set of a (S,R)-bimodule for which <=- determines a partial order and for which <=- is a lattice. We analyze the relation <=- by examining the associated Baer (p, q)-sets. Finally, we apply our results to C*-modules. Examples are provided to illustrate and delimit our results.
Description
Keywords
Baer bimodule, Baer ring, C*-module, Partial order, Projection invariance, Science & technology, Physical sciences, Mathematics, applied, Mathematics