TL;DR
This paper explores various *-ring orderings, extending classical properties of *-positive elements and Blackadar's property (SP) to broader classes of *-rings, including *-accretives and Blackadar *-rings.
Contribution
It generalizes classical *-ring properties to new classes of *-rings, providing a broader framework for understanding *-positivity and Blackadar's property (SP).
Findings
Generalized *-ring orderings for *-accretives.
Extended Blackadar's property (SP) to broader *-ring classes.
Connected properties of Rickart and Blackadar *-rings.
Abstract
We examine a number of *-ring orderings, generalizing classical properties of *-positive elements to *-accretives. We also examine *-rings satisfying versions of Blackadar's property (SP), generalizing some basic properties of Rickart *-rings to Blackadar *-rings.
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Taxonomy
TopicsRings, Modules, and Algebras · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology