Weaker hypotheses than regularity suffice for left-right transfer of C4* properties in rings, with identified obstructions from square-free phenomena and permanence under matrix passage.
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The C4, C4*, strongly C4*, and semi-weak-CS conditions on modules are Morita invariant.
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Left--right Transfer for $C4^{\ast}$-Rings Beyond the Regular Case
Weaker hypotheses than regularity suffice for left-right transfer of C4* properties in rings, with identified obstructions from square-free phenomena and permanence under matrix passage.
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Morita Invariance, Categorical Obstructions, and Dimension Transfer for \texorpdfstring{$C4$}{C4}, \texorpdfstring{$C4^{\ast}$}{C4*}, Strongly \texorpdfstring{$C4^{\ast}$}{C4*}, and Semi-Weak-CS Modules
The C4, C4*, strongly C4*, and semi-weak-CS conditions on modules are Morita invariant.