On the Index of Nilpotency of Semigroup Graded Rings
We find the index of nilpotency of a strong supplementary semilattice sum of rings, R=\tdsp\sum α∈ Y R α , where Y is a semilattice, when each R α has index of nilpotency≤ k . Then we find the index of nilpotency of R when it is graded over a rectangular band Y and each R α has index of nilpotency≤ k . These results are generalized to normal band graded rings. Further, we find sufficient conditions for a ring graded by a semilattice of nilpotent semigroups to have bounded index of nilpotency. We also show by examples that these conditions are necessary in some cases.
Gopalakrishnan, Hema. "On the Index of Nilpotency of Semigroup Graded Rings." Semigroup Forum 62.1 (2001): 146-158.