TL;DR
This paper establishes that if a ring possesses a test module with finite upper complete intersection dimension, then the ring must be a complete intersection, linking module properties to ring structure.
Contribution
It proves a new characterization of complete intersection rings via the existence of specific test modules with finite upper complete intersection dimension.
Findings
Rings with such test modules are complete intersections
Finite upper complete intersection dimension implies strong structural properties
Provides a new criterion for identifying complete intersection rings
Abstract
A ring with a test module of finite upper complete intersection dimension is complete intersection.
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