Weak diamond, weak projectivity, and transfinite extensions of simple artinian rings *

Abstract

We apply set-theoretic methods to study projective modules and their generalizations over transfinite extensions of simple artinian rings R. We prove that if R is small, then the Weak Diamond implies that projectivity of an arbitrary module can be tested at the layer epimorphisms of R.(c) 2022 Elsevier Inc.

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Keywords

• Weakly projective module
• Weak diamond principle
• von Neumann regular ring
• Semiartinian ring