A note on the class of sober rings
Saeid Jafari, Ernesto Lax
TL;DR
This paper introduces the class of sober rings, explores their properties, conditions for their existence, and their relationships with other ring classes, supported by illustrative examples.
Contribution
It defines the new class of sober rings and investigates their properties, conditions, and connections to existing ring classes.
Findings
Sober rings are characterized by specific algebraic properties.
Necessary and sufficient conditions for sobriety are identified.
Examples demonstrate the behavior and scope of sober rings.
Abstract
We introduce the class of sober rings and investigate it through several key results, highlighting connections to some other known classes of rings. We analyze sufficient conditions for a ring to be sober, as well as necessary conditions. We also provide examples to illustrate the behavior of this property.
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Topics in Algebra · Algebraic structures and combinatorial models