TL;DR
This paper characterizes when certain algebraic constructions form valuation rings and explores their properties, including the property, providing a comprehensive understanding of their structure.
Contribution
It offers necessary and sufficient conditions for valuation rings formed via trivial extensions and investigates their property, advancing algebraic theory.
Findings
Characterization of valuation rings via trivial extensions
Conditions for property in valuation rings
Insights into module-based valuation ring structures
Abstract
In this paper we provide necessary and sufficient conditions for to be a valuation ring where is a non-torsion or finitely generated module. Also, we investigate the property of the valuation ring.
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Taxonomy
TopicsRings, Modules, and Algebras