On \(\phi\)-\((n,d)\) rings and \(\phi\)-\(n\)-coherent rings (Q6617096)

Let \(n,d\geq 0.\) The authors introduce and study the class of \(\phi-(n,d)\) rings. It is shown that the \(\phi-(0,0)\)- rings are exactly the \(\phi\)-von Neumann regular rings, the \(\phi-(0,1)\)-rings are exactly the hereditary rings and that the \(\phi-(1,1)\)-rings are exactly the \(\phi\)-Prüfer rings with \(Z(R)=\mathrm{Nil}(R).\) It is also shown that the \(\phi-(n,d)\)-rings are \(\phi-n\)-coherent. They also introduce and study the class of \(\phi-n\)-coherent rings.