Pure projective tilting modules (Q2187925)

The authors give answer to pure projective version of Saorin's Question. The answer is positive for Noetherian commutative rings, arithmetic rings in Proposition 5.5, a ring over which every pure projective module is a direct sum of finitely presented modules in Corollary 4.8 (as example is a Krull-Schmidt ring), commutative rings in Theorem 5.7. The answer is negative for rings with an idempotent ideal finitely generated on the left satisfying certain conditions given in Theorem 6.3, as example the universal enveloping algebra of semisimple Lie algebra \(sl(2,\mathbf{C})\).