Semisimple rings graded by inverse semigroups
Let \(S\) be an inverse semigroup, and let \(R=\bigoplus_{s\in S}R_s\) be a faithful \(S\)-graded ring. If all group-graded subrings \(R_G=\bigoplus_{s\in G}R_s\) are semiprimitive (semiprime) for all maximal subgroups \(G\) of \(S\), then \(R\) is semiprimitive (semiprime). If all group-graded subrings \(R_G\) have no nonzero nil (locally nilpotent) ideals for all maximal subgroups \(G\) of \(S\), then \(R\) has no nonzero nil (locally nilpotent) ideals; a similar result holds when each such \(R_G\) has no nonzero nil right ideals.
scientific article; zbMATH DE number 1214127
scientific article