Gr-coherency of polynomial rings and \(G\)-graded rings
Let \(R\) be a ring with identity. The authors prove that the polynomial ring \(R[T]\) is gr-coherent when regarded as a \(\mathbb{Z}\)-graded ring if and only if \(R\) is coherent. Also it is proved that a ring \(R\) graded by a finite group is gr-coherent if and only if \(R\) is coherent.
scientific article; zbMATH DE number 1406299