Chain conditions for rings with enough idempotents with applications to category graded rings
Let \(S\) be a ring with enough idempotents, and let \({e_i}_{i\in I }\) be a complete set of idempotents for \(S\). The author proves that if \(S\) is left/right artinian (noetherian), then \(I\) is finite, and for every \(i\in I\), the ring \(e_iSe_i\) is left/right artinian (noetherian); moreover, under an additional condition, the converse also holds. This result is applied to certain category graded rings.
scientific article; zbMATH DE number 7870863