On the finite separability of finitely generated associative rings
Stanislav Kublanovsky
TL;DR
This paper establishes criteria for when finitely generated associative rings are finitely separable, focusing on monogenic rings and torsion-free PI-rings, linking algebraic properties to their separability.
Contribution
It provides necessary and sufficient conditions for finite separability of monogenic rings and characterizes finitely generated torsion-free PI-rings in terms of their additive groups.
Findings
Necessary and sufficient conditions for finite separability of monogenic rings.
Finitely generated torsion-free PI-rings are finitely separable iff their additive group is finitely generated.
Link between algebraic structure and separability in associative rings.
Abstract
We find necessary and sufficient conditions for the finite separability of monogenic rings. As a corollary, we prove that a finitely generated torsion-free PI-ring is finitely separable if and only if its additive group is finitely generated.
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology