Let R be a noncommutative ring, is every projective R-module torsion-free? or, for what kinds of rings (or algebras) the answer is affirmative?
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2What do you mean by tosion-free? Is $R$ at least a domain? – Rafi Nov 16 '23 at 17:14
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Since projective modules are flat, the solution at the attached question would answer your question. – rschwieb Nov 16 '23 at 18:31
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thanks Rafi, I think R should be a domain, then Z(M) will be a submodule! – Kami sh Nov 17 '23 at 05:22